I really like this guy. We have a connection and we get each other. I want to be with him but I can't date and he's my bff's ex. What do I do?

Well, if you can't date ... You can't date.  That's all there is to it, at this point.  So you just remain friends until you CAN date.  Then you ask him out.

It doesn't matter if he is your bff's ex ... EX means your bff has no say in his relationships, anymore.