I have no idea what this sentence means:
"Bishop then--jauntily stepping out a little with his well-shaped
right leg, as though he said to Mr Merdle 'don't mind the apron; a
mere form!' put this case to his good friend:..."

Part of the formal wear of bishops looked like an apron. I think the idea is that the bishop wants to be treated by Merdle as if he were a layman.

Bingley