What you're saying about that SHE thinks it's unprofessional, could be a 'shit'-test.
She's just testing you and doesn't want it to go that easily, women love the game. And quite frankly, I myself don't even like it when a girl just gives it all right away. There has to be an secret element...
If you think she's into you and acting strange around you to get your attention, just let her behave how she wants and be sure to be busy during work with a happy attitude. That way when she tries to get your attention, you can ACT like you didn't hear her or didn't see her (doing something to get your attention). Act is in capitals because it's important to ACT good. Don't make it seem like you totally ignored her. BUT overall, when she tries to get your attention, you should have fun WITH her! You also have to tease her.
Secret element... Maybe tell her that people/co-workers can't know about your relationship and she has to act like you're not fucking each other. That way when you're alone for 5 minutes she'll wanna do crazy shit and then you both have to act like nothing happened, etc... Ofcourse I don't know what kind of girl it is, but from what I'm hearing the girl secretly wants you. And that should be your mindstate from now on.
I think that's the situation you kind of want... No relationship yet not only sex.
And I wanna know what happens , so keep this thing posted!
GG