Hi Kent,
I'm not sure if you're joking or not, but I don't think the gym will help. You don't need to overpower the bike; you need to keep out of situations in which you find yourself needing to hold up the weight in an awkward position.
One caveat to the above would be in case you are actually very slight of stature and the bike is just too big for you. That is possible, but only you can answer that.
I don't mean to sound preachy (but it IS Sunday), but one needs to be so much more decisive and diligent on a bike than in a cage. You need to anticipate where you are going and what you're going to do ahead of time. To make it even more difficult, you need to be anticipating all of the stupidity around you in people and their vehicles.
Without knowing you at all, I would suggest: 1) Exploring if the big does not match your body, or if it far outmatches your driving ability, and 2) Get into a driving course. Maybe you've taken the Basic MSF or not, but you just need more time and experience.
Friend, I don't mean to offend, but dropping your bike three times in these circumstances should be a sever wake-up call for you. Put aside your pride and take a look at root-causes!
Good Luck,
J