How do you play it when a “taken” girl at the gym keeps coming up to talk to you?

I’m looking for some pointers on what to actually say in this situation.

There’s a girl at my gym who keeps coming up to talk to me. She told me she has a boyfriend, but her behavior makes it pretty clear she’s interested. She finds reasons to walk over, lingers in conversation, smiles, and she’s usually the one who starts it.

I’m not trying to break them up or create drama. I just want to handle the dynamic smoothly, keep the tension fun, and use it as a chance to sharpen my social game.

So here’s my question: Should I lean into a little flirty banter, or stay more neutral and let her keep driving the energy?

Curious what the best approach is here when she’s “taken” but still clearly invested in talking to you.