I think there are two important things you should consider
1: The whole frame as it is right now
I think you need to flip the script and make her work more for you. Right now, it always leads to you asking her to come over. And she's in a relationship.
How about going
a bit overboard with the text banter for now and see if you can make
her ask if she can come over instead?
What I mean is - hit the brakes. Stop asking her to come over for now.
Take a
little time off to banter and flirt with her on text, just for the sake of it.
Maybe she will open up more. See what she has to say. Ask her about it. Share small bits about yourself if she asks - just enough to make her wonder about you. And when her mood is right and/or her bf is doing things wrongly, she might want to come over, all by herself
Or maybe you can sense a high note where it makes sense to ask her to come over. But then stop with the hard closes and suggestions of coming over right away. Figure out her schedule first and work it from there. She's not available to you all the time
2: How you think about and handle the objections a girl raises
Even if you did all that work I just wrote above, she may still "object" to come over. But these objections are the real tests. This is where you are supposed to show her what you are about. Objections can show up regardless of your fuckboy frame
How do you respond to her objections? And what does your response tell her?
Let's say her objection is that you probably won't listen to what she has to say
A:
Do you go "nah, nevermind" and surrender completely?
Then she knows you just want to play it on easy mode and that you are being selfish. You're not in it because you value her. So let's make her feel you want her...
B:
Do you go "come on girl, of course I will listen to you, don't be silly" or similar?
Now she knows you want her. But it doesn't look beneficial to her in any way... she has emotional needs too. How can it look beneficial to her?
C:
How about sticking to the flirty and mutually fun vibe you have created at this point?
Do you make a pinky promise like
@Will_V suggested? I might even try this myself at some point!
Or another fun and absurd promise?
"I will hear your whole life story
then I will show you this painting/poem/song that I just finished after a looong time"
She knows you want her since you are being persistent. But you're being silly about it while implying that you will meet to connect. And she gets a reward for opening up. What's not to like for her?