Not sure that this is a language use question so much as it is a question of etiquette and manners.
In general terms if you invite someone then you should be ready to pay the bill and avoid a potentially awkward situation. You can either arrange with your server beforehand that you will pay the bill and they are not to bring it to the table, or simply be the first person to ask for the bill at the end of the meal.
If you have been invited then you should always be ready to pay your bill when the time comes.
Basically, politely decline if you can't cover yourself unless someone has specifically told you in advance that it's their treat.
If you go out for dinner with people and ask who's paying the bill it may seem a little ungrateful and invitations may stop coming!
However, it's certainly correct to ask "How will we split the bill?" or "How much do I owe for dinner?" If the bill has been given to one person (or one person has asked for it) then you should try to be subtle about this and go directly to that person and ask them.