The position comes from Reuben Fine's Basic Chess Endings, still to my mind the greatest chess book of them all and one that probably deserves a better fate than being parked, as mine is, next to the loo. (Although in my case, this does entail sharing shelf space with a translation of Virgil's Aeneid in a probably vain effort to impress our visitors.)
I very much doubt that I could find the mate in thirty-three, though I'm fairly sure that I could do it inside fifty. I learned how to go about it at a training weekend for Hertfordshire juniors in, I'm thinking, 1983. My tutor was none other than Nigel Povah, now of Guildford. He taught us how to manoeuvre the Black king into the "wrong" corner (of opposite colour to the bishop) before performing a delicate sequence which forces the king into the other corner, where he can be mated. You probably have to know what you're doing, as at one point the Black king seems to be escaping from the side of the board.
Being less of a utilitarian and more of an advocate of learning for its own sake, I can't really complain that despite having known, for quarter of a century, how to mate with bishop and knight, I've never had the chance to do it in practice. Not in a tournament game, not in a blitz game, not even in an offhand game. Ironically enough I've had it done against me, at St Albans in (possibly) 1994.
I've also seen it not done, when my friend Sean Terry was on the wrong end of the material balance in a 4NCL game. You can see his opponent fail to win by accessing Chessbase Online Database and inputting Murphy for White and Terry for Black. White's 75th move in particular demonstrates that he didn't know what he was doing. He was - had he known it - quite close to completing the first of the two stages outlined above: but that he was, however, baffled, is confirmed by the fact that his 76th move involved reversing the move that he'd just played.
Embarrassing, no? I think it'd be pretty hard to work it out against the clock, even for a good player, though in truth my St Albans opponent claimed not to have known the technique beforehand. In a blitz finish it'd be even harder. So - can you do it? Can you do it inside fifty moves against your computer? And have you ever had to do it in practice? Have you ever seen it done? Or seen it not done, for that matter?