He's definitely one angry young man when we meet him, and he pretty much stays that way for most of the play. He comes to the Army looking for his girlfriend, who was apparently recruited by the Army's Jenny Hill. He's super peeved at having "his" girl snatched up from him in this manner, so he ends up punching Jenny—and Rummy, too, when she gets in his way.
Barbara refuses to get ruffled by his awfulness and violent behavior, very matter-of-factly reciting his list of crimes back to him in a way that actually seems to make him feel super guilty. She also tells him she wants to save his soul.
Barbara doesn't quite pull that off, but Bill does end up feeling badly enough about hitting Jenny that he decides he'll go confront his ex-girlfriend's new boyfriend, a professional fighter; in his view, it's only fair that he get his face bashed in a bit to compensate for what he did to Jenny:
...I'm goin to Kennintahn, to spit in Todger Fairmawl's eye. Aw beshed Jenny Ill's fice; an nar Aw'll gi t me aown fice beshed and cam beck and shaow it to er. Ee'll itt me ardern Aw itt her. That'll mike us square. [To Adolphus] Is thet fair or is it not? You're a genlmn: you oughter knaow. (2.206)
So, he's hardly a knight in shining armor and never ends up converting, but at the very least he ends up feeling bad about his violent behavior toward Jenny—though he claims he doesn't feel bad about hitting Rummy.