I don't think this could be called bullying tbh. It is upsetting, I agree, but it is not bullying.
You cannot make a child want to be friends with another child. Just because someone does not want your child in their friendship group and gives them a wide berth it does not necessarily make them a bully.
To me, bullying is persistently directing unpleasant behaviour, violence or intimidation towards a person, as a form of sport or as a way of exerting control through fear. It is the act of seeking the victim out in order to make him feel bad.
More often that not, when children frequently leave another child out of a social group it is not necessarily a conscious or deliberate act to hurt the child - it's just that they don't particularly like having him around, and therefore do not bother to include him. That's all.
And if he asks to join in he may be told no, because that's what happens in the grown up world - we can choose our own friends and we are not forced to socialise with people who don't float our boat.
It is heartbreaking if you are that child - but it isn't bullying.
Now deliberate ostracising, and encouraging others to actively turn against and ignore an individual with the sole purpose of making him unhappy - that is bullying. but I don't think that is what has happened here, in the case of the party invites.