Much will depend on what bone was broken. There are a lot of them in the hand.
Having gone through that though back in 2003 and rushing the rehab (hey, we were losing the Tour), I can tell you that it is NOT going to be worth it for the sake of league bowling. I still have occasional pains more than a decade later. The fracture I had was in the cluster of bones near the wrist...the actual location was not pin-pointed until an MRI was done after the original set of x-rays.
All of that being said, I was able to throw competently within a matter of a few weeks, although it was about five weeks if I remember right before I rolled a full three-game set in a league environment. Tournament barely two months later and the US Open the following month. I still remember Jeffrevs comment from the stands towards the end of the third day of that one...It was late in the day on C squad and I'm having to drift the ball return and had the front seven or eight and you hear 'broken hand, my ass' immediately after my shot.
BUT...the next week in Terre Haute, there was not enough Vicodin in the bag to mask the pain.