You could simply not wear anything.

[He pulls his coat back tentatively, but yes, it's clotting. He sits back, grimacing a little as he shakes his coat out. He's going to have to . . . well, never mind what he'll have to do with this coat, it's not pretty and it's not dignified.]

You're going to have to treat this more, but you shan't bleed out on the way home.