Hi,
The Boot Menu and Windows Advanced Options are different things. Usually, the boot menu appears before Advanced options (the Boot Menu only appears automatically if you have multiple operating systems installed, and ask you which one to boot. It is skipped if you only have one OS installed).
The BSOD in the installation process might mean two things:
- either the CD you're installing from is broken (try to find another disc)
- either some of your hardware is malfunctioning
The BSOD should contain the error code, written in CAPITAL LETTERS, somewhere at the top of the screen. That is the message that gives the reason why the system crashed. What you posted (Stop:...) is only the memory location where the fault occurred, so it's not of much help on it's own.
As for reinstalling BD after re-installing your OS, yes, it's possible. Just reinstall BD, use the same key (be sure to have your original license certificate, or whatever). Also, activate BitDefender using the same BitDefender MyAccount as you did with the current installation.
Despite all your problems, I hope you'll still enjoy Christmas. Merry Christmas!

Cris.