Sorry to hear about your injury. I wish you the best!
As always, it’s advisable to work with your doctors and those you trust, as each person’s body is unique. For what it’s worth, a family member of mine has multiple herniated, bulging, and/or crushed discs in their back. It’s caused decades of problems and for years kept this person off their bike. What finally worked for them was finding a bike with a very specific geometry that aligned their back in a way they could pedal without inflicting excess pressure on the injured sections of their spine.
It took months of trying every bike we could get our hands on and making all sorts of modifications to stack height, reach, pedal position, saddle, etc. In the end, though, one was a clear winner and now this family member is back to riding almost daily.
No one here will be able to help you with this unfortunately. A competent PT will determine your “motion preference”, meaning some people get symptom reduction with flexion (or bending) of the lower back and some will get symptom reduction with extension (arching) of the lower back. Everyone is different.
And a word of caution for everyone. Herniated discs are a common finding on lumbar spine MRIs and only sometimes are contributing to symptoms. For the spine specifically, imaging and results and symptoms only rarely coincide. Many of my patients have herniated discs in their lumbar or cervical spine and only a few ever present with lumbar spine disc herniation type pain (meaning they can’t even sit it makes their leg and back pain so bad, cant bend at the waist at all, etc…). So patients with multiple disc herniations will present as a flexion or bending preference to motion - even though in theory, that would make their symptoms worse.
Don’t ever let a clinician begin giving you exercises with a thorough examination that is based only on imaging findings as that is improper and inappropriate care. An exam based on symptom provocation and movement is the only way to go.