Action.

Even though he became Emperor Consort and got some very delicious powers, he didn't change much. He still feels the need to get out of the Palace on his own, to visit the wilds and to be BangSul, above everything else.
LianBi has a lot to do and surely can't spend his whole time with him, which leaves him alone for most of the day. Basically, after being done with the few duties he has and the very rare meeting requests from Court and people, he is left to wander on his own and just wait for the evening, when LianBi will be done with duty and, after dining with his children, will finally come to him.
And now that Gamja even got her totally perfect boyfriend, he has even less to do and feels very lonely. All he can do is to visit JiHwan and TaenQi, but he doesn't want to choke them with his presence either, so he literally ends up wandering like a tormented soul all over the gardens...

That matter about prostitutes, though, does bring some fresh air to that choking situation he was ending up into. Not just because he is a perv! Maybe some little investigation could keep him busy for some time. He is confident it wouldn't take him much effort to get in touch with one, after all, isn't he pretty much exactly what they'd be looking for? A rich noble who wants to be found.
Without even mentioning his idea to LianBi, at least for now, since he'd feel way too embarrassed if he failed after telling anyone what he has in mind, he leaves the Palace on his own. He wears a luxury hanfu, but somewhat more discreet than the official Emperor-Consort-robe or the Imperial-Family-robes. He doesn't want to look like a commoner, just a noble but not too exaggerated, thinking that it'd scare any prostitute from him.

It's late afternoon, almost evening. He is in Taifuan, around the centre. When he made all his calculations he failed to think about one details: what are really the most likely places where to find prostitutes?
He walks among the food stands, trying to look as natural and casual as possible.