What is the Proper Move?
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I don't think it would be smart to capture the bishop because it opens up a file for the rook.
is this a game you're currently in?
No, it was a live chess game. I eventually resigned because my response to that move ruined my king protection.
I wouldn't ask for advice on a current game.
You can't allow the bishop to stay. 7. hxg6 hx6g 8. Ng5 preparing Qxg4 next. If 8... g3 then fxg3 opens a big attach agains F7 with your bishop and rook and knight
6.. h5!? is a nice trick, but not so dangerous. You can play 7. Be2 or 8. d5 and then 9. Be2, and you have a small advantage. Otherwise, 6. h3 is unnecessary, you can play 6. d4, 7. Be3 etc.
mathismall is correct. 8. Ng5?? results in an even trade of material, but your kingside would be screwed. However, 8. Qb3! threatened Bxf7 then Qe6 mate. He would have to defend it, with the queen you can just follow up with Ng5 and his queen is overworked. If he defends with the knight, you are still fine because the knight blocks the rook temporarly. This would buy you enough time to play Qxb7 regaining your material and a pawn (which you will probably promptly lose) before your king ran from the kingside.