The latter. "お + the -masu stem of a verb + する" is an honorific, more accurately to say, a humble form（謙譲語）. Thus, お願いする is a humble form of 願う, as same as お尋ねする（尋ねる）, お会いする（会う）, お出しする（出す）, etc., and in these cases, the recipient of the respect is the the recipient of the action(the target of the verb), not the doer of the action(the subject of the verb).