As other people have said, max heart rates do not follow the 120-AGE equation. I had a friend who was 48 and I think I once pushed him up to 210. I know another guy who at 54 had a hard time getting to 160. Both guys were in reasonably good shape. There is all sorts of individual variation.
I would give you a few caveats. You should get checked out by a physician. If you have any real doubts of your cardiovascular system, a stress EKG would not hurt either. Another thing, over the years, I have seen a bunch of accidents caused and/or suffered by cyclists who are exercising close to maximum levels. I know a couple who have actually passed out whilst red lining on the bike. Passing out whilst riding does not strike me as a really safe thing to do.
But that being said, if you get involved in any group ride on any weekend, there are some riders who treat it as their RACE. And they have GOT TO WIN. If it was very easy to kill yourself by pushing things too hard, we would have dozens of cyclists die in the state of FL each and every weekend. So you can push yourself awfully hard without any real damage.