I was having this problem too, and the stupid/simple solution was that I was running one instance of VMWare Player (for linux), which forces you to suspend one VM in order to return to the library and open another.
Each time I suspended a guest VM, its network would shut down, so I was trying to ping a suspended VM from the one that was currently open, which was unsuccessful because it was suspended, not because there was something wrong with the bridged network.
My solution was to simply open multiple VMware Players. That way I have a VM open in each Player, and now all my VM's can talk to one another.
Maybe this will help someone.