Under-Promoting to a Bishop

So here's something for the members of this esteemed community to do: consider the following conundrum and see if any of you can provide a definitive answer!

There are a number of well-known situations and puzzles where the only way to win is to (under) promote your pawn to a knight, and I know of at least one where it has to be a rook (see below). However, does anybody know of a situation where the only way to win is to under-promote to a bishop?

I've been discussing this problem with a chess-playing friend (actually, a very strong player) and his thought is that it's actually not theoretically possible ... does anyone know if this is the case?

Here's the rook situation: (fen: 7K/5k2/8/4R3/8/8/5p2/8 b - - 0 1 - sorry, the 'insert diagram' thing isn't working!) If 1: ... f1=Q, then 2: Rf5+ forces Qxf5, stalemating the White King; the only win is f1=R!

Over 10 years later I answer your question

I found this video where at 8:14 they discuss a puzzle with bishop underpromotion: https://www.youtube.com/watch?v=KkYJV3Pj9AY 

There are several such cases. Here is one