I rarely solve the "hard" puzzle of the day. I just do not have the patience. So I usually try for maybe 5 minutes at most, then start guessing if I had not figured it out. In this case, I did manage to solve it in just a couple of minutes.
My thoughts progressed as follows
1. The king is currently stalemated. I looked for ways to check.
2. The h4 rook is not doing much, but can check in 2 moves.
3. Black can queen the b-pawn. also providing luft for the king.
4. The a5 knight can go to c5 then a4 giving check and covering b2.
5. If Nc5 immediately, black can defend a4 with the bishop (1...d6).
6. So then I looked at blocking the b-pawn. Of the 3 choices, only the bishop block seemed reasonable since it maintains the stalemate and the rook and knight move do not.
7. The bishop block move also provides 2 ways to mate using the h4 rook.
8. I could find no defense against the rook mate threats that also stopped the knight mate threats. I confess, I did not look at every possible black first move choices.
9. So Bb1 must be the first move.
10. After black's response (in my case, the computer played Bf7) 2.Nc5-Na4 was obvious.
11. After solving and clicking on "OK", then clicking on "|<" I went through all the black defense options and saw that there were many different defenses that require different second moves by white that I had not analyzed before selecting 1.Bb1 as my solution.

So as it turns out I did get lucky.

I don't think so ... I think it's a matter of skills ...
I think skills make the beauty of chess.
I think, for example,that patience is one of the skills some people have to achieve a better ELO.
And I believe that the will to develop them also it is ...
But, opinions are like the nose: everyone has one  
Of course: nice puzzle. Thanks