。
May I have the check, please?
Literal
Bill [object-を] please.
A polite request for the bill — same content as the casual 勘定書を頼むよ but a different register. お願いします is the standard polite request formula, attaching to a noun (here 勘定書) to mean 'please [arrange/give/do] this for me.' A clean illustration of how Japanese scales politeness: the core content is identical, but the social signal shifts entirely through verb choice and sentence ending.