I used to be intimidated by league players. I'm not nearly the bowler you are. My average is around the 150 range. My wife had bowled in leagues before we had met and asked me for years to join a couples league with her but I always refused because I didn't think I was good enough.
This past summer, some friends of ours talked us into joining their league. It is the best thing I ever did for my game. I am more interested in bowling and improving my game then I ever was. On top of that, we have a great time.
Some leagues are more serious than others. You will just have to "shop" around until you find the one that's right for you. Ours is a handicap league with mixed teams. They balance the teams based on average and handicap the matches. This prevents teams from recruiting a "ringer", and the lower skilled players (like myself) are actually contributing to the team rather than just taking a roster spot. They also split up couples so there is no bickering during games
With a 200+ average, I don't think embarrassment will be a problem. Just get out there and bowl. You WILL NOT