Wayne, I know everyone's balance system is different, but I say go for it on the bike riding if you can. This subject is also near and dear to me. I was a pretty avid bike rider, as I had done several road biking events (with colleagues)of 100 miles in length before my AN surgery. For incentive/motivation, 2 weeks before my surgery I bought me(with my wife's approval) a fancy new Italian road bike. I figured that if I invested that much money in a bike, I'd really be motivated to get back to riding as soon as I physically could. I was fortunate with my surgery and I was able to do 25 mile rides as soon as 3 weeks post op. I'll admit that I was a little scared getting back on the bike after surgery, but after the first couple of miles I was fine. I know it sounds weird, but I feel like I have better balance riding a bike that I do walking slowly or standing still.
Right now, I'm running more than biking(because it's too cold(for me) even in Houston to bike in the winter), but I plan to get back more on the bike come spring time. I'm registered to do my 7th consecutive MS150(180 mile, 2 day bike ride from Houston to Austin to raise funds for MS) in April, so I determined to continue....and I would encourage anyone to try biking, running, surfing, paddle boarding, etc....get out there and give it a shot. I think you'll find it to be fun and invigorating, not to mention helping to improve your physical fitness. Enjoy.
Patrick