Depends where you are. Cheque please? Could we have the bill please? Mostly, though I just get a waiter or waitress's attention & make a sign as if writing on something.

I use " can you bring me the check please" more than bill, however both are correct. The bill I associate it more with a utility or credit card payment kind of situation.

_the_ bill, _the_ check. You want your one, not just any one.