Both of these lines are faster, though the first isn't forced.
1. Rxb7 Qxb7
2. Qg8#
1. Bxb7+ Qxb7
2. Qg8+ Qb8
3. Rb8#
Not forced but with the move you used:
2. Qg8+ Bf8
3. Qxf8#
This is forced in four:
3. Qxf8+ Qb8
4. Rb8#
And in your combination I most like mate by 4. Rb2# :)
My mistake, I'd forgotten about the bishop.