@Rogier Haest Can you confirm what was the port number you have performed the test? As the service bus document talks about 5671,443,5672 but depending upon the type of WCF relay binding you are using you can refer to this document for the port number that you need to perform the test.
You can do the nslookup on the namespace name to know the IP address of your namespace name i.e. nslookup yournamespacename.servicebus.windows.net
You can also use Port Query Tool to test the IP address along with the port number to verify if the connection is blocked at your client network.
If the above test are passed then you can use netmon traces to reconfirm whether your application is connecting to the same port/IP address for which you have performed the test. The suggestion would be engaging your network team to assist you further.