I really think he is better off not being friends with this bully. Also, if the mother of the bully decided to ignore his behaviour rather than challenge it, it shows where he gets it from.
I, like you, am also not great at playdates and social meetings, but for the sake of my son (who has a tendency to be a little timid) I have pushed myself to organise things. The more you do it, the less painful it gets! For Ds's first 2 or 3 playdates in our house I was so anxious that DH had to be around (just to paint a picture for you), now I don't mind one bit.
Two books I have bought which I recommend are: how to be a friend(for the children to read, my 6 year old likes it), and the unwritten rules of friendship (for parents to read, really good to the point with excellent recommendations)