Any further interactions she'll try to get the party aid her current goals and undermining the other brides. Her identity and the other bride's identities as vampires stay hidden until the Dinner with Strahd.
After her identity has been revealed, she does not care for the party and she knows she is too powerful for them to pose any threat. If interaction is necessary, she is open about her desire to please Strahd and how dangerous the other two Brides are. She won't do them any harm if they don't cause any harm to her.
Irregardless on the statblock, Ludmilla isn't stupid. She'll run and heal if she hits 1/2 hitpoints. This will probably frustrate your players but she knows her limits and doesn't have a ego to satisfy. She'll also is smart and will stay on the move frequently, trying to stay out of reach of any martial characters. Note:If she's expecting a fight, she'll come with 4 Barovian Witches with her as backup that she sends out first as the front line while she stands from afar aiding her allies and hurting the party.