Gotta say that if you’ve got a day in The Lake District …
… go to Buttermere.
Walk round the lake (4 miles - flat) and have beer and food at either of the two pubs.
The quality of the scenery is out of all proportion to the (lack of) difficulty of the walk.
Good lord that is beautiful, not Swiss Alps “I’m gonna start singing the ‘Hills are Alive’ like Julie Andrews” gorgeous, but wow. How in the heck do I fit that in??!!
Y’all have been so kind to help and offer suggestions while putting up with my nonsense, so here is my first semi-coherent update:
Yes this means we are going to miss all my favorite childhood book tour (Wind in the Willows, Winnie the Pooh, Peter Rabbit, Mouse & Mole “half a banana now, half a banana later”, Canterbury Tales ). Sorry can’t stop the nonsense 
But seriously those are my favs and my kids favs.
Looking for suggestions on this segment:
as I continue to plan out the front-end of trip.
From Bath to York you could visit Stratford Upon Avon for some Shakespeare, then a short hop onto Naseby for some English civil war sites.
The UK has loads of Cyclosportiv type events. Often based at the many national parks and all the favourite routes including those roads used for national events. Event calendar below.
I’ve been thinking about doing something similar. Am wondering what you will do for a bike? Take your own, buy a new one, to bring home or flog while there, Hire if so who from, etc? How are you going to transport it, campervan?
Bath to York has a few options. You would take the M5 motorway towards Birmingham (possibly stop off at Stratford for Shakespeare?) and then a choice, either M1 direct North towards York/Leeds or M6 towards Manchester and then the M62 over the Pennines. M6 option could include a detour to Ironbridge perhaps, broadly half way.
For the full ancient history tick I’d add a stop at the Uffington white horse on your way from London to Bath . The views north across the Cotswolds from the top of the hill are quintessentially “english”
White Horse Hill | Oxfordshire | National Trust
Between Bath and York I’d suggest a detour to Chatsworth house for Afternoon Tea and a chance to stretch your legs around the stunning formal gardens.
Chatsworth
This is ambitious but I think you know that by now - seems like quite a few others have warned against trying to do too much so I won’t frame what I’m saying as a suggestion/warning. What I will say is that the abundance of warnings doesn’t surprise me. It’s almost a predictable trope that Americans visiting here will try to take on way more than they have the capacity to really fully experience.
As long as you know and understand what you’re getting then don’t let any of us scare you off of your dream itinerary though. I think we’ve all just seen lots of visitors commit to the whirlwind version and then leave wishing they’d spent more time on fewer places. But if whistlestop is your style and you’re going into it with your eyes open then don’t let us stop you! 
I’m from California and have been in Glasgow for 15 years now so I see those travel patterns quite a lot from friends and family (and I did the same too when I first arrived!) I think the thing that @splash tried to highlight which is really difficult for us Americans (especially west-coasters) to comprehend is that sizes/distances/etc. just don’t scale in the way we expect. Best example I can think of in California is comparing San Francisco to Los Angeles - because SF is a Victorian pre-car city the amount of history/variety/travel-time packed into each square mile is just way more dense than LA.
But the UK (and Europe) is an even more extreme version of that difference - most of the civilization on this island had been continuously inhabited for over a thousand years even before San Francisco got started, which means the scale of distances here isn’t just pre-car but also pre-industrial-revolution. That’s how you end up with accents that are so wildly different across distances of as little as 20 miles - anything further than a day’s walk for a horse and cart meant people just didn’t interact with each other often enough for their speech patterns to align (which also meant they’d end up with complete localised histories/cultures/artifacts too).
And to take it even further - a huge amount of that highly localised history and culture was already in place pre-printing-press. So even if the East Coast of the US had a thousand years to establish before the industrial revolution instead of a hundred, it would still have ended up more homogenous than anywhere in Europe just because of the efficiency of how information could be distributed across larger distances.
So if you have to zoom in 2x to get from LA to SF in terms of scale, you’re going another 2x to get to the East Coast and then another 2x again to get to the ‘old world’. (Obviously those are highly exact and incredibly scientific numbers that are definitely 100% accurate 
You get the idea though.)
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Sorry, ended up on a bit of a tangent there! I’m keeping it because I think even more than informing how I might plan an itinerary I find that lens really helpful just in terms of my understanding of what I’m seeing and experiencing regardless of how much or how little time I choose to spend in a place. 
If I were to make one specific suggestion I’d maybe say to leave that second “Scotland” day undefined til you get here if you can bear to do so - you might find you just want to stay an extra day in Edinburgh and leave the rest of Scotland for another visit when you’ve got time to spend a few weeks just exploring north of the border. Enjoy your trip, wherever you end up spending your time!
Digressing, but if you’ve not been you’ll have to go to the California which is circa 19miles north east of Glasgow, some good cycling roads round there
anniversary trip, my wife doesn’t ride and not planning on throwing my leg over the bar of a bike unless its easy/cheap and more convenient than taking a bus/metro.
Yes I get it. The sticking point for many is “full or deeper experience.” I’ve given the analogy that we are looking for a smorgasbord, or in Spain we are going for tapas instead of a full meal. We aren’t planning to move to the UK, this isn’t a where should we live trip (we are doing those right now in the US). It’s a deliberate and conscious choice. My wife wants to make “the one trip” to the UK & Ireland and sample a subset of the most iconic and important historical places.
As an experienced car traveler, the Bristol-to-York drive looks unappealing and nothing of particular interest to see along the way (other than Conwy/Snowdonia which is out of the way). And it is only $70 (x2 = $140) to fly from Bristol to Edinburgh. So I’m thinking of flying from Bristol to Edinburgh, hire another car, skip York, and do Vindolanda as one of the day trips from Scotland.
It is really not “along the way” other than generally North to start with, in fact as you say is out of the way, I would say very out of the way, totally in the opposite direction once you get so far North, and the roads are extremely slow, A and B class roads.
There is lots interesting stuff between Bristol and York, but in depends on your idea of interesting.
There are lots of interesting places between those two cities (obviously - you’re talking about driving through half of England), but you’re not going to see them from the motorway.
Sure, that’s why I said of particular interest (to us).
FWIW…
Before posting on the forum, I reviewed the key info spread over 1800 pages in these 2 books:
and started with the red Must See list in the front of the GB book:
and we watched a collection of YouTube travel videos.
Then I looked at his suggested car trip:
Looks interesting, but ain’t nobody got time for that except the retired!
Its a not bad car trip he suggests but you actually miss out quite a bit! Enjoy what you do see and maybe by autumn (fall) the UK summer will have actually arrived 
Ironbridge is pretty uninspiring, other than 5 minutes, unless you vistit all the museums, Bliss Hill Victorian Town, China Works, Tar Tunnel, Pipe Works, Jackfield Tile museum, museum of the Gorge etc.
It then becomes from an interesting 5 to 10 minutes for the toll house and bridge to a really good two days… amazing place but only if you have the time to see most / all of it and you then get to understand the place and its history.
I take it for granted a bit, as it is 30-40 minutes away from me, but do the whole thing every 5 years or so, and every time learn something new or see something we’ve not seen before.
I see Glastonbury and Wells is in one of those books/guides, the Tor and Glastonbury is weird and interesting imo. You can see the tor from miles away across the Somerset levels, I mentioned it earlier. Can also spend an hour or two in Cheddar and the Cheddar Gorge if based in Bath / Bristol.
Like this thread, given me some ideas, never been to York.
Lake District is beautiful 
but that is not really on route. Beatrix Potter homeland.
Read about the Tor, and wanted to ring up Peter Gabriel and have him write a song about it! If you aren’t old enough or familiar… Solsbury Hill (song) - Wikipedia
That is North-east? of Bath, never been there, but will if passing, actually the family has been talking about going to Bath.
I was referring the Glastonbury Tor
a short walk from Chalice Well,
Cant remember but I think its a Druid place of significance, people baptised their children there in water from the Springs…
It also a bit hemp and witchcraft, it is like the early 60s in modern day, weird, but that is just my “take” maybe. Difference people will experience it differently I guess.
yes this one:
made me think of Peter Gabriel and nearby Solsbury Hill.
Ah okay, I get the reference now, kind of near by, i thought you’d misunderstood.
Ps, never made it to the top been 3 times, the wife refused to walk any further the time we specifically when to the Tor (but I never said that on this forum) To be fair to her it was starting to rain.
Which reminds me, hope you get the right weather for the mood of where you are, some places are special in the sun some in the mist.
no, I’m captain random keep up, would ya? LOL.
