34 Bxb4 is necessary to try to get the bishop out into open play. The problem is that after 34 Bxb4, Black has left f2 wide open to mate threats. Black can immediately play Bd4 which is a killer, the bishop cannot be taken due the resulting royal knight fork, and moving the white king only offers up mate after Qh4. For some reason Black decides that Kg7 is necessary to stop any back rank games, but really I think this is unnecessary, as the king seems reasonably safe, while both the black queen and black bishop control the a1-h8 diagonal.
35 .... Qh4 (or Nh3+ and Qc1+) is coming now that the route for the white queen to take the Knight on f4 is blocked nothing can stop black's infiltration into the white king's position. The best would probably be to retreat the bishop back from b4 to e1, but really this wont help too much as it defeats the object of taking b4 in the first place.
Also as the black queen can easily dance round the bishop on g4 to attack the white king, the white bishop on g4 is really nothing better than a big pawn, as it will take it quite a while to get to a better square. Especially as black simply isn't going to give white that kind of opportunity...