very nice!
Bishops are stronger than rooks
Just because of this, you can't suppose that bishops are stronger than rooks. In this position however, your bishops were much more powerful than your opponents rooks due to the fact that the rooks lacked mobility, and weren't doing much on those squares, but your bishops were 'slicing' through the safety of your opponents king and therefore you had the upper hand.

Nice. Although as someone said, it was more of a rook, 2 bishops and a Queen than just two bishops. Either way, pretty mate.

The final combination using a pin is very elegant!
I Don't particulary like blacks 7... Na5 (sidelining the knight for no apparent reason) and 8... Be6 and would probably annotate those moves with ?! instead of !?. Although material is nominally egual after 12. bxa5 I think that white's two knights should be stronger than blacks rook and pawn in this particular position, especially as blacks rooks don't have any open lines. 12... f5? opening the king and weakening the e6-square must also be a positional mistake.
In this game I checkmated someone with Q + 2 bishops vs. Q + 2 rooks. (1.c4 transforming to King's Indian)