Thanks for all the great advice. What I have learned so far......My short wheelbase bike is very twitchy, which is part of the problem. The other problem seems to be that I am not drinking before my ride - being sober means I'm not relaxed enough resulting in grabbing the bar too quickly.
I will first try the beer solution, since that is less expensive than a new bike.
Thanks to all of you who suggested I am a coward. Now that's motivating!