How could the Bishop's faith be characterized as "rational moral faith" according to Immanuel Kant?
Excellent question. Kant, in essence, was eschewing organized religion for allowing man to feel be his being "holy" by attending service, whilst all the while behaving in an unChristian way to his fellow man.
The Bishop, however, is a Kant supporter. The Bishop places the church below good works in his estimation. He believes the church should be open, at all hours, to all people, no matter their sin. He says that the belongings of the church are those of the people, and gives them away freely. He lies to the gendarmes and gives Valjean enough silver to become a new man, even though this is fraudulent; he does so, because he knows that Valjean need not be socially accepted to be a good and virtuous man. When he does give Valjean the silver, he tells Valjean that he (the bishop) has bought Valjean's soul for God - not for himself or for the church, but for God.
In short, the Bishop does all he can to put "natural religion" above the power of the church.