THIS ANSWER ASSUMES THAT IF A PIECE CANT MOVE IT CAN'T THREATEN
With this assumption
White cant win
If somebody could help me embed a chess game that would help to visualize but white basically has two options
Get king to B5 to free rook at B7 or
Get king to B6 to free rook at B4.
First 2 turns for white are
First 2 turns for black are
White moves KB5, Black takes the rock at B4, since the King is frozen by the pawn this is a legal move and black has check mate.
White moves Bb6 and again black takes rook at B4. This leaves only the white pawn free as the king and rook cannot be separated so black wins again.
Since white eventually has to free one of the rooks to win, black can just stay within one square of B4 and he can win as outlined above regardless of any other delaying moves the white king makes.