Can White draw?

No!!!

The King can't move, the rook can either kill the pawn on a2 resulting in black rook b1 mate or white rook can move anywhere along the a-file and, again black rook goes b1 - white rook must kill it and then a2xb1 mate. The bishop can't prevent anything either so, therefore, white cannot draw.........or can he?!!!

I presume we're facing the board the correct way and whit King and Rook are on the 1st rank rather than the 8th rank?!

Yes the board is the way it is shown.
White's rook and king are on the first rank...
And the only way to draw here would be through stalemate but can it be done?

Originally posted by ilywrin
And the only way to draw here would be through stalemate

Ah, yes this too.

1. Bh4
If 1. ...Rb1+ 2. Be1

2. ...Rxe1+ 3. Rxe1 wins for white
2. ...Rxa1 is stalemate

1. ...Kxh4 Kxh2 is drawn I think

Does black have better responses?

Originally posted by Schumi
1. Bh4
If 1. ...Rb1+ 2. Be1

2. ...Rxe1+ 3. Rxe1 wins for white
2. ...Rxa1 is stalemate

1. ...Kxh4 Kxh2 is drawn I think

Does black have better responses?

Originally posted by ilywrin
Well, there's 1...Rb2!?

Yes, I concur 🙂 For any that are curious find why 1.Ba5!? fails...