Are you absolutely sure you installed the App without the firewall module? - Meaning that you did the custom install and not the express? Double check under windows processes & see what's running. Just check in BD UI --> SCRIPT MODULE & configure it - I'm not too familiar with Bdefender, but it's worth a check.
I also use BD10IS and it has never blocked Media Player nor Windows search. Are you sure it is BD that is the cause. Just hover your mouse pointer over the BD icon and you will see which modules are active. A right-click will enable you to disable the firewall, if it is active.