Verify that the SSH service is offered on that IP by performing a port scan. If you're not knowledgeable with port scanners, just download the Nmap pack with frontend from http://nmap.org/download.html and perform a standard scan.
If the service is not up, you need to talk to the IT staff in charge of managing that server.
Odds are, SSH is running but not on the default port. A Port scan should reveal the current listening port.
Another possibility is that the SSH daemon on Server B restricted login to certificate users. In that case, you need a public/private SSH key pair.
You can create one following this tutorial:
Once you have your key pair, you can contact IT to tell them to add your public key to Server B authorized certificates.
How to contact IT
If you can't find the SSH listening port like this, you can formulate a request to the IT staff in this manner
"I need to be able to transfer files via SFTP to Server B. Can you please put the SSH service up if it isn't and tell me the listening port? In case there is a Whitelist set up, please add my Server to it
In the event that Server B is using a certificates authentication scheme, please add my public key to your authorized keys list (attached to the email).
It is possible Server B has a list of allowed ips to connect to the SSH daemon, the "whitelist" part of the request should take care of that.
While you're at it, ask for a user/password if you don't have a centralized authentication backend.