I agree with others on going ahead with the party. However, most 7 year olds, especially today, are capable of understanding much more than a lot of parents think they are. If they weren't they wouldn't be "school age." So, I would talk to her and explain that you had thought of cancelling the party due to her poor behavior but decided not to because... other kids, parents etc ... but NOT because you changed your mind about her behavior. I also wouldn't give her the main presents yet... just a minor one or two... and would tell her why. I would tell her exactly what present she's not getting until she learns to respect others more with her behavior.
I would also ask your BF if he agrees with letting her have the bike on those terms later. If so, he should be the one to explain why to her and, by all means, he should be a part of your talk with her. I don't agree with others that he has no say in how she behaves in his home. He lives there too and does contribute to her welfare. I think that if you don't respect him as a human being you'll be letting a 7-year-old run rough shod over both of you and children do what works... that's just smart really... if she see she can drive a wedge, she will.
I had my boys in counseling... long story... but the counselor said kids were actually happier when constrained. Its very fearful for them too feel they have too much independence and power. When I thought of it... yeh, that would be pretty scary. Anyway, sometimes they act up because they are scared that way. The counselor said they need more, not less, structure to feel safe.
Edit: PS.. thought about that right after I sent and LOL... that's why some of us need a HP.