Consider the following diagram:
4k3/3b4/6p1/1p6/pP3P2/P7/8/4K3 b
Black is Pawnitized
Here, despite his extra bishop, Black cannot win this ending. This is because all of White's pawns are on opposite-colored squares than the color of the bishop. Here, we say that White has "pawnitized" Black (rendered his bishop useless). This terminology is due to siggemannen.
Therefore, if your opponent has an extra bishop, you still have hope to draw. Consider:
8/p7/2p2p2/5n2/2k2P2/2P5/P7/3KBN2 b
Black to Move and Draw
Here, Black's first priority is exchanging knights: 1. ... Ne3+ 2. Nxe3. Now, Black has two pawns sitting on dark squares that must be pushed to light squares. Which one should be pushed first? 2. ... f5. Of course. Otherwise, White would play f5 himself, fixing the pawn on f6, where it will get exchanged later for White's bishop and White would win. Now: 3. Bf2 a6 draw.
8/8/p1p5/5p2/2k2P2/2P5/P4B2/3K4 w
Drawn
Now, Black will just leave the pawns where they are and shuffle his king around. White can't make any progress.