BitDefender indeed is a very good protection. If I get it right you purchased BitDefender after your computer got infected, that's probably why it can't get rid of threats. It's always best to install antivirus software on a clean computer.
I suggest that you should download SUPERAntiSpyware. Install it in Windows Safe Mode (that's important!), not in Normal Mode as you installed Bit Defender. To get into Safe Mode you hit F8 key as soon as your computer beeps once when turned off. Then choose Safe Mode with Networking. Update SUPERAntiSpyware before running a scan. Select full scan for best results (be prepared to wait long though, full scan can take up to half an hour to complete and even longer).
SUPERAntiSpyware will remove detected threats without asking you for a license, you don't have to pay anything to get rid of infections. Once your computer is clean, you can safely uninstall SUPERAntiSpyware. But it is a good idea to keep it for occasional scans.
Here's my review of SUPERAntiSpyware:
Most probably it will resolve your troubles with trojans.