Bagoas has a system. This system involves using interesting architecture as area markers (as sign posts mean nothing to him, and he can't read). Maaaaybe they could bump into each other on one of his frequent outings?

It would be a meeting of the 300-ish BC Eunuch Looking Like a Lady and the 2xst/nd/rd/th Century Digital Dream Girl. HOW COULD IT POSSIBLY GO WRONG? :D