Does Texas law require that a husband be financially responsible for a wife that committed bigamy and the marriage was annulled

Well, bigamy is when you have more than one spouse, correct? I would say that if you still had one husband - the marriage to the second would not have been legal. So, saying that - I would say that the 2nd husband wouldn't be financially responsible - since he was legally never a husband.

From which husband view point, is this husband #1 who is and was the legal husband, or is this husband number #2.

Husband number 2 was never legally married to the wife, since if she was already married. I guess an annulment would have been a way to go, but a court ruling voiding the marriage license would have been a way to go also. ( unless this is what you did and is calling it an annulment)

But since for husband number 2 there was no legal marriage, there is no responsibility at all. In fact there may be costs that husband 2 could sue wife for because of the fraud,

I thought an anullment made it as if there was never a marriage at all; meaning no spousal support or division of assets etc. as opposed to divorce which is dissolution of a legal marriage.