Since we got cable broadband I've just left the connections active -- if I want or wanted to block a program from having access I'd just forbid it from having access in the security software's firewall. With Bitdefender Total Security clicking the star shaped icon in the upper right of the Firewall box opens its settings. From the main Firewall Settings dialog you can click Application rules to set access, one app at a time, or by turning Paranoid mode on, it'll tell you whenever software wants to connect.
I wasn't aware Bitdefender itself actually needed access for more than updates. Maybe it checks the license, but I don't know why it would need to check the license in a free version? There's a Bitdefender update service that starts with Windows -- it's in Admin Tools -> Services. You can't stop it, & you can't change its startup type to manual from automatic unless you boot into Safe Mode -- do that & I have to start it manually from Services before Bitdefender will notice it needs an update & before it'll update.
That said, the Total Defense version at least has a Game Mode you set after right clicking the tray icon. When Game Mode's on, it won't auto update & it won't scan every file you or your software accesses. A Lot of times something will seem to be taking too long [e.g. copying a file or folder], & checking vsserve.exe in Task Mgr., it will show some activity -- turning Game Mode on usually stops that & whatever task then seems to work normally. The downside I've found is that sometimes when I turn Game Mode off it won't always turn Auto Update back on in win7. On my wife's system it's been pretty good at detecting when she's playing a game, & then goes into Game Mode automatically, turning Game mode off when she closes the game.
I don't know whether any of that will help or not.