In case you were not aware. If you set a rule in Notes to forward the email it is server based so it will forward even if your client is not connected. Sorry you are not able to get a connection on the BES server
To get your server name you can look in your location document. You can access this in your notes client down at the lower right hand corner. Usually by default it says office. Click here and select edit current. Then go to the Servers tab. Your server name is listed in Home/Mail server. However, this may not be the DNS name.
Does your company offer the webmail interface for lotus notes? If it does then typically the address for this service would give you the DNS name for the server. You could always try adding this to BIS and seeing if the POP or IMAP protocol would work. Unless they have specifically turned these services off when setting up the server they will be running. The name and password would be what you use to login to webmail. It could be the same as your Notes password but they are NOT synced by default.
BEWARE--Attaching to the server using POP or IMAP will show in the server logs so if they are monitored your actions will be seen by whom ever reviews the logs. As well as any logging that is done on the Company firewalls.
You might want to talk with your supervisor or take the BES admin to lunch and ask if you could be included on the BES server.... There is almost always a spare license or two laying around until needed...