OK guys, USBC got back to me and heres the official rules on my question:
There is a difference for leagues and tournaments.
In leagues, according to rule 118b, a right handed bowler must always bowl right handed. Similarly a left handed bowler must always bowl left handed. This is regardless of whether the competition is scratch or handicap or classified.
In tournaments, according to rule 328, in handicap and classified tournaments, once the bowler has taken his/her first shot, they will continue to bowl with that same hand. In a scratch tournament that is not classified, the bowler may alternate hands at any time.
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Jason Smith