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I have been curious for a while about this ending...and it seems that the side with the rook will inevitably win as long as the king and rook stay off the color of the bishop. If anyone wants to look at my hypothetical game below and comment, feel free, especially if you see ways in which black could have forced a stalemate.
1.Kd2 Kd7
2.Kd3 Ba6+
3.Kd4 Kd6
4.Rc5 Bb7
5.Ke5 Kd8
6.Kd6 Bc8
7.Rb5 Ba6
8.Rb8+ Bc8
9.Ra8! Ke8
10.Rxc8+ Kf7
(White will eventually win with the K+R vs. K endgame technique.)
That position should be a draw with correct play. Esentially, the bishop can prevent the stronger side's king from gaining the opposition - although I'm not confident enough in my technique to show you a correct line from memory. I'm sure someone else will step in soon. 🙂