I dont use handlebar tape on my TT bike which is what I use on the trainer. I use a few small portions of skateboard grip tape. On the trainer, I throw a towel over and don’t have any issues with discomfort. bare bar and towel might slip on each other a bit though.
I generally do this all winter. It’s a lot easier to clean up if you sweat a lot, like me. It’s a little annoying when you get a random nice day and have to do a tape-less outside ride, but if I had a dedicated trainer bike I would personally keep it untaped.
I agree with the above, no bar tape on my dedicated trainer bike. I used to run bar tape and no gloves, but the bar tape started to stink and when I removed it the corrosion underneath was worrying. Better to run without tape to avoid these issues.