4

Is it possible for white to do a queen-side castle in this situation and capture black's bishop? Assuming both rook and king haven't moved, of course. The rook would be capturing the bishop in this case.

[FEN "8/8/8/8/8/8/8/R1b1K3 w - - 0 1 "]

I've been trying to find examples or rules one way or the other, but I could not.

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No, such a move is illegal, because one requirement of castling is that there be no pieces (of either color) standing between the king and the rook. From the FIDE Rules of Chess, 3.8(b):

  1. Castling is prevented temporarily:

    a. if the square on which the king stands, or the square which it must cross, or the square which it is to occupy, is attacked by one or more of the opponent's pieces, or

    b. if there is any piece between the king and the rook with which castling is to be effected.

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