Lost and don't know what to do about relationship

Hi, a bit of background. My boyfriend and I have been together for a while, and the last couple years have been really good. A few months ago he kissed another girl he works with, but we talked and decided to stay together as I said as long as it was a mistake but I was the one he actually wanted to be with we could get passed it. I say things were good, but we always had a problem with communication and this has helped us realise we need to talk more. We did our best to get past it, and he spoke to her and said nothing was going to happen between them and that I had every right to contact her(which I did). She said she didn't want drama and wanted to forget about it. But She keeps messaging him periodically asking him to meet up for drinks etc, he's ignored them all. But now she keeps going on my facebook liking and unliking stuff etc. I told him and he said just to block her what can she do. I feel like I'm being made out to be the bad guy by her, and I just don't know what to do. I don't want to lose a relationship that is good, and we've both said we want to work through the bad stuff. I'm just at a loss as I can't control what she does, and he can't leave the job atm so she isn't going away anytime soon. I just feel like most people would take someone ignoring them so much as a hint to stay away, and saying it outright to her would just make things even more awkward/hard since we still have to be around her and she seems quite immature so wouldn't be able to listen to someone being honest. Him telling me to block her makes me feel like he thinks I'm the problem, but I'm not sure if that's just me feeling paranoid. I am scared me continually being bothered by this will drive him away, but I don't know how to not be bothered by her.

This sounds like a difficult situation you are facing and it seems you are handling it well. If you want nothing to do with her, then you should block her. I understand how you would want your boyfriend do make her leave you alone, since he is the one that created the problem, but you also have power here. In an ideal world, what would you like to see happen?