No, the official Firefox installers from http://getfirefox.com do not bundle any additional software, such as AdAware.

Did you see a (unauthorized) page where Firefox is being distributed with additional software? Or did you want a malware scanner?

Sorry, what I meant was "adware", not AdAware. Do you know if it does?

No, the official Firefox installers from http://getfirefox.com do not bundle any software of any kind, whatsoever. Firefox is completely free software.

Why do you think that Firefox is bundled with adware?

Appearance of adware/malware after you installed Firefox is probably just coincidental.

If you do have malware/adware, I suggest you run a scan and remove it. One scanner is:

http://www.malwarebytes.org/mbam.php - Malwarebytes' Anti-Malware