So”right”:
I don’t know the parameters of chukas hagoyim, but it does not cover everything they do.
Most of the daily activities we do are straight from the goyim.
What we wear. (And no, Polish nobles weren’t Jewish.)
What we eat. (Polish peasants weren’t Jewish.)
How we speak. (Bad German and bad English are both Goyish.)
Basic social norms. (We didn’t invent shaking hands.)
The tools we use. (knives, forks, shovels, guns)
So yes, if the custom was to bow to your date, I would probably do it, and I don’t think it would be chukas hagoyim.
Call me back when you destroy your engagement ring.