How do you deal with a subway flirt, that is giving you a chance to become her boyfriend right away?

I'll try to break it down as easy as possible:

approached a girl on subway, we talked a bit, exchanged numbers at my stop, I left. 

I texted, "This is me, we just hooked up on the subway". Later she replied, "Are you serious about meeting up with me, because I'm in the middle of  a relationship and it hasn't ended yet. So, was thinking if I should give you a chance"

Basically, she wants to end her relationship anyway and needs to know that I'm not just a flirt. What can it mean?

I wrote her right away to schedule a date, to see how it goes then. She said she's busy with work. I replied that we can meet during coffee break, she said that in her job is impossible.

I know she sounds flakey, but it could be that she doesn't want her boyfriend to find out.

She'll be out of town for a a week. What do I reply now?

I want to say that, "it's ok, I'll see you once you get back. Have a nice trip"

Not to seem more needy and that she knows that I have a rotation of girls (which I actually do)

This can be a shite-test from her, I never know.

If anyone experienced the same, guys, how do I deal with it?

Thank you.