I don't have a specific method, but I have some general tips.
Herd the king to the corner while being aware of skewers and stalemate traps.
Learn some of the K+QvK+R studies to have a strategy in key positions.
Attempt to separate the rook from the king.
No. There is no position you can construct in which the black king is in check (has to be from the bishop), white only has king and bishop and the black king can't move.
The closest you can get is this:
[fen "k7/1BK5/8/8/8/8/8/8 w - - 0 1"]
And the black king can move to a7.
Non-royal king is a combination of [0,1] leaper (wazir) and [1,1] leaper (fers) and in fairy chess called a erlking. About erlking, see my book Fairy chess endings on an n x n chessboard (2017), page 545.
The ending of king + erlking against bare king on board 8x8 is won for the stronger side and the longest win has 18 moves. Also the ending of two erlkings ...