To update...
Was trying to do the duels with Handmaiden after Telos, but before going to Dantooine.
On Dantooine, took her (and playing as LS) everywhere and gained influence (specifically, when refusing to help the mercenaries), finished Dantooine and got back on the Ebon Hawk. Tried doing the duel again and this time it WORKED... although I'm not influential enough yet to get past the third duel.
So in the end, can still call this a glitch because she shouldn't accept your challenge to train if you don't have enough influence to beat her (at least that seems to be what is happening). Solution: gain some more influence with her and try again later.