The Bloomberg application is most definately MDS based. If you can't establish MDS communications with your BES the application will now function correctly. A good way to test this is to try using your Blackberry Browser. Unlike the Ineternet browser this will route communications through your MDS. The application does also require that you have allow inbound and outbound connections set to "true"
A good way to check where in the communications chain your having a problem is to try and login, then look for the PIN # of the Blackberry in your MDS logs. If you have error logging on the Bloomberg MDS Gateway set to high you should see a corresponding entry right afterwords in the MDS gateway logs. If there is no entery in your MDS logs at all, then the application is not able to talk to the MDS service because of a configuration problem, be it on the device or in the IT/Application policies.
When in doubt give the Bloomberg IT staff a call. You'll have to be transferred a few times till you get to someone on the Blackberry staff, but trust me those guys rock!