Look for opportunities to make a favorable exchange. Somewhat paradoxically, one of the biggest advantages of holding the two bishops is that at any moment you can exchange one of them. The point is to simplify into an endgame where your remaining bishop is superior to your opponent's remaining knight or bishop.
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[Event "rated untimed match"]
[Site "?"]
[Date "1974.??.??"]
[Round "?"]
[White "Mikhalchishin"]
[Black "Kozlov"]
[Result "1-0"]
[Annotator "David Hayes"]
[BlackElo "0"]
[FEN "2r2rk1/1b2qppp/pp1p1b2/2np4/P2NPP2/3PB1RQ/1P4PP/3R3K w - - 0 1"]
[SetUp "1"]
[TimeControl "0"]
[WhiteElo "0"]
1. Nf5 Qd8 2. Bxc5 { This knight must go to prevent it from returning to
defend black's king via e6. } 2... dxc5 ( { Black can try: } 2... Kh8 3. Bxd6 dxe4 ( { Black can try: } 3... Rg8 4. e5 { Trapping the black dark-squared bishop. } ) 4. Qh5 g6 5. Qh6 Rg8 6. Rh3 Rg7 7. Nxg7 Qg8 8. Nh5 Bd4 9. Be5+ Bxe5 10. fxe5 gxh5 11. Rg3 Qxg3 12. hxg3 { White wins with a large material advantage. } ) 3. Qh6 g6 4. Rh3 Re8 5. Qxh7+ Kf8 6. Qh8+ Bxh8 7. Rxh8# 1-0