A King and Bishop alone cannot mate the lone King...but a King and two Bishops can! Let's see how...
The following two diagrams illustrate the typical mating patterns:
As you can see in the first diagram, the Black King occupies the dark square in the corner of the board and is in check from White's dark-squared Bishop. White's light-squared Bishop and the White King are covering all of the squares to which the Black King might retreat.
The mate in the second diagram is much less frequently seen, but it certainly is mate! White's light squared Bishop and King are blocking every avenue of departure while the dark-squared Bishop delivers the fatal blow!
When delivering this checkmate, be careful to avoid stalemates once you force the lone king to the edge of the board or into the corner. Be sure to provide a square to which the lone King can move if you are not going to deliver a check.
The following diagram illustrates one possible stalemate:
With White to move, it's mate in one by attacking the Black King with the dark-squared Bishop. With Black to move, however, the position is a stalemate because the Black King cannot fulfill its obligation to move.
So how to deliver the mate with the two bishops. In the following position, it is white to move and mate in three moves. Be careful to avoid the stalemate!
Click here to see the solution.