I'm guessing that the OP had their tickets issued prior to 15 Nov 2010 so it would be 2 pieces. I'm also willing to wager that, by checking in at the Biz counter as they are traveling on a Biz ticket the OP would be afforded the 2 bags anyways, even if the first segment is in Y.

Probably have to go to the M+M forum to get confirmation on that, however.