Unless you have access to a lathe - or a mate with one, then carefully selected, suitable sized sockets can be used along with a piece of HT threaded rod and nuts. You need to find a socket for pushing which is slightly less in diameter than your new bush and another socket on the other side of the arm which is large enough inside to accept the old bush. The problem with most sockets is that they have a radius at the ‘mouth’ end. It might be worth removing this radius with a grinder so it fits flat to the bush - don’t spoil one that’s part of an expensive set though - best to buy a cheapo.
Make sure you only push on the outside of the bush to avoid the possibility of tearing the rubber.
Hope this makes sense, I can’t get into the toy cupboard to take a pic.
Ian