Has anyone in their reading come across Latin words for to ‘hit on’ in the sense of speaking or behaving in a way that shows they want to have a sexual relationship with you. [informal] ‘She was hitting on me and I was surprised and flattered’. A synonymous phrase is ‘to make a pass at’ i.e. to do or say something that clearly shows one wants to begin a romantic or sexual relationship with (someone) ‘He made a pass at his wife's friend’. I can think of three words ‘attrectare, petere and captare but I’m sure there are more. I’ve looked in J. N. Adams’s The Latin Sexual Vocabulary but couldn’t find any.
The closest you might get to “flirt” is probably blandior, blandiri = to charm, sweet-talk; and for “make a pass at,” rogo, rogare, which of course just means “ask,” but in the right context is similar to “hit on.”
There’s Ovid’s much-quoted quip (Amores 1.8.43):
Casta est, quam nemo rogavit.
A chaste woman is one who’s never been asked.
And here is Ars Amatoria 1.707-712, where you see not only rogā, but also verba precantia and blandas preces.
Ā, nimia est iuvenī propriae fīdūcia fōrmae expectat sī quis dum prior illa roget. Vir prior accēdat, vir verba precantia dīcat. Excipiet blandās cōmiter illa precēs. Ut potiāre, rogā. Tantum cupit illa rogārī. Dā causam vōtī prīncipiumque tuī.
Here’s how I’d translate this.
A young fella who waits for a girl to hit on him first is putting too much faith in his own good looks. It’s the man who’s got to make the first move, the man who’s got to win her over; she’ll be nice to you if you just sweet-talk her a bit. If you want to get a girl, ask her—she just wants to be asked! Tell her what you like about her, and how you came to feel the way you do.
(This passage, by the way, is one of the few in the book that actually gives good advice).
I’ve never seen it, but I wonder of you could also just be blunt and say something like: venerem petere ab aliqua / aliquo.