To clarify things, let me say that "When the BD makes a Bishop move, it does not jump over other pieces, it really makes a normal FIDE Bishop move. Only when the BD moves two squares Rookwise can it jump over obstacles."
Notice that this piece is colorbound. If it starts the game on a White square, it will never see a Black square all game long.
This piece is usually a little bit stronger than a FIDE Rook, for most of the game, in most positions; and potentially noticeably weaker than the FIDE Rook in some late endgames.
I usually use a physical Rook to represent this piece on an ordinary board with an ordinary set of pieces (this piece has a value of Rook), but I can understand if you prefer to use a Bishop.