I suggest you go with ethical behavior.
- You want to date a woman with a BF.
- You don't want to wreck a good thing for her.
- So you could do the respectful thing and ask them both to seriously consider if they could be willing and able to partcipate in a "V" polyship with her as the shared hinge.
- Could NOT choose to be disrespectful and become her cheating partner, start lying, and start going against your own grain/ethics. That's a good way to ding your own spiritual health.
1) The dating issue?
Could ask up front and honest.
- Find out their answers. It all lines up? You could all launch something forthrightly then.
- It doesn't line up? You stay friends and cushion that small disappointment with the fact that in your own behavior you were honest and ethical and you can still be friends. Forthright friends. Yay.
2) The cheating issue? Could get to the bottom of her shirky.
How does her inviting you to become her cheating affair partner demonstrate "deeply committed to my BF" behavior? It doesn't. It makes her seem shirky. And her Word now being shaky?
Could note if you are not actually asking him anything -- and it's all filtering through her and she's blocking you having direct communication with him.
You could re-examine what she said to you about "one night stands are ok" and "bf not good with YOU being the bf" because I suspect your shared sex already.
If she said their agreement was "casual ok, check in for more?" She got the sex share with you from the sound of it. And now that you are at the time and place of "check in for more"... [I] she doesn't want to.
That second bit could be a partial truth. BF is not good with you being the new BF not because of your "YOU-NESS." But because she made you her "unwitting one night stand cheating partner" by lying about that agreement even existing. And BF would not be crazy about ANY cheating partner. She's inviting you think it's YOU -- so you will agree to stay silent?
Could it be that she rather invite you to be a cheating affair partner because she doesn't want to be caught out by either BF or YOU? And the "damage" she is actually worried that honesty at this point in time will "out" is her own poor behavior? She has treated you both with less than honest behavior and less than respectful behavior and the consequence could that both of you could be pissed with her poor behavior if either finds out?
Smells fishy. But could still go with your ethics and sort this all out. Ethics is not for wimps.
I suggest you go with ethical behavior and get to the bottom of the shirky and ask for his "willing and able" honestly.
Then at least you in YOUR conduct are playing like Jedi -- you want to date a woman with a BF, so you ask them both up front if they are willing and able to polyship like that or not. You are worth dating respectfully, right?
If she gave you false information at the start you and BF could both be cross with her. But she could own her own behavior.
Choose well how you want to behave in each of those issues. Because you
get to own YOUR behavior.
We are all free to choose. We are not free from the consequences of our behavior.