even just a few blocks if you needed to to go to a store if they would not let you drive a car.

You don't mention what condition prompts your question, so it's difficult to answer directly. Ability to ride a bike is stored in the implicit/procedural memory part of the brain, so cognatively speaking, riding a bike is possible even when explicit/episodic memory is impaired. That said, it would not be advisable if spatial orientation has been affected. If you can't drive a car due to problems with spatial orientation and/or reflex impairment then riding a bike is also not advisable. If you are seeing an occupational or other therapist they would be able to answer your question directly based on thier evaluation of where you currently are in your recovery.

If your going to ride a bike, I wouldnt go off any curbs or go over speed bumps...just to avoid rattling your head/brain around. Stay on a flat surface like the sidewalk or the street. Watch out for dips and such, you know.

I rode my bike around outside a few weeks back...I didn't notice any negative effect.

I haven't done much bike riding in the last 10 years. But I have a unicycle that I have ridden sporadically since 1972. I tried to ride it recently and the reactions needed to stay balanced were not there. My legs knew what to do but my reactions were too slow and haphazard.

I would think you could experiment riding locally where there is no traffic to worry about.

Wear a good helmet and be careful. I got my worst concussion from a bike accident when I hit some sand.

Concerning riding a bike when you can not drive a car; I have a valid driver's license but have to limit my driving to my good days. On my bad days, I do not drive and I would not feel confident to ride a bike either.
btw, I have been tested by a driving/rehab specialist and was approved to drive even though I had a melt-down in a congested intersection and needed to pull to the side of the road.

My best to you.