In almost all situations, rooks are stronger than bishops. Perhaps you will be able to use a bishop to skewer a rook, or to pin a rook to a queen or the king.
Here's another way for a bishop to dominate a rook. The following position occurred in game 13 of the World Championship match between Bobby Fischer (playing black) and Boris Spassky (playing white).
White has just played Bf6-e7 with the threat of Be7-f8. If the Bishop reaches f8, the Black Ra8 will not be able to capture the white g-pawn when it queens.
To prevent Spaasky from queening the pawn, Fischer played Ra8-g8, and Spassky then sealed in the rook with Be7-f8. As you can see, the White bishop (with a lot of help from the advanced g-pawn), is completely dominating the black rook!
