I have had bulging discs and I have had four back surgeries. My first was in the 80s, when endoscopy had not yet been invented. The last three surgeries were easy to recover from. The first, I am still having problems with. That disc ballooned out toward my stomach. The only access was to cut the muscles to the right of my spine. Since then, I have suffered death with lower back muscles that will never be normal. I have accepted this. My only salvation is exercise to keep those muscles loose and functioning.
Each morning, I ride a stationary bike for 30 minutes. I pretend I am biking my way to KMart for their blue light specials. Remember those?
Riding your bike may be your only salvation, also. my doctor states my bike-riding can do nothing but help my ailing back muscles.
I see no problems for you and your bike. The key is to keep it up. Go for it.