Thanks for the replies.
I never really wanted to be besties with Anne - far from it actually - I just want us to be able to be polite in each other's company, maybe all be able to attend the same event if we all wanted to go without it being uncomfortable, and communicate when we need to. Maybe I am underestimating how hard I'm trying and I'm being overbearing, but I don't interact with her online or ask her to spend time with me one-on-one, only go over when Bob asks and has checked with her first which isn't very often, and really all I would hope for is that she take a few minutes to say hi when I'm there, and use basic manners when interacting with me.
Why is this such a big deal to me? Having no hope for more life entanglement with Bob in the future is a major problem, so if me and Anne can't work something out in the future where I'm not the one making all the effort then I don't really know how me and Bob will pan out. I'm not okay with seeing him only twice a week for the rest of my life, put it that way.