I have been facing an issue with VMware which is unable to ping host machine from Guest Machin, but I'm able to ping guest machine from host machine.
Note: Here one more interesting matter is I could able to ping my host machine from guest machine with NAT network, but I couldn't ping my guest machine from host machine.
Your question is not clear at all.
In any case, you might wish yo specify what OS you are using in both nodes.
Firewall issues? You could try to disable Windows firewall for instance and locate where is the issue.
Could you give some basic data of the IP address of both nodes when the set up is in bridge mode?