Whenever doing business in a shop that accepts payments via bank transfer,
could the shop take the money first from the bank account before any carried
cash is used? It's quite annoying to drop your mithrils off before buying
something.

Well if you're referring to the ship-related shops, most of them have a
different command for using the ship-bankaccount, just use it and it will
always take it from the bank.
If you ment the other shops, that'd mean that we couldn't collect trashcoins
and shop with those anymore, at least I do that quite often.