With the dubious security reputation Bitcoin already has, you're already on thin ice with regards to this sort of thing. My gut says that by asking for banking

With the dubious security reputation Bitcoin already has, you're already on thin ice with regards to this sort of thing. My gut says that by asking for banking passwords, you hurt yourself more than you help yourself. If you're looking to get users into the door more quickly, you could borrow a page from LendingClub, who will let you deposit from a credit card, but only when opening a new account, not afterwards.