At this age I suspect he is not a bully he just doesn't have the tools to deal with situations in a manner that doesn't involve hitting, pushing etc. Most kids go through this stage around 2-3 when parents usually step in and teach them a more appropriate way to deal with socializing with other children.
Either the mother doesn't know how to deal with it, or she doesn't see there is anything wrong with what he is doing. If I was in the situation, I would play referee for a bit,
Your child has toy other child pushes to take it, tell him that it isn't nice to push, explain why it isn't nice, take him by the hand to his mother and tell her that child pushed and you thought she should be made aware, tell her what you have said to him and then leave it at that. By the same respect, if your child took toy and got a shove for it. Don't automatically side with your child, explain to child that he shouldn't shove your child but also explain to your child he shouldn't take toy if someone else is playing with it. Then as both children were in the wrong take toy and put it somewhere else.
Hopefully by seeing this "mean" child will start to realise that it isn't the way to act. Now I realise that it shouldn't be our place to parent someone elses child and I wouldn't normally get this involved but IF the mother really has not an idea hopefully by bringing it too her attention that it is behavour that bothers other mothers she might start to do something about it.
Kirsten