No it's not normal, 20 seconds is way way too fast. You do however need something better as the free version a very badly hacked about version of an obsolete package, even Bitdefender don't recommend it as primary protection :-
"BitDefender Free Edition is an on-demand virus scanner, which is best used in a system recovery or forensics role. If you are on an "always-on" Internet connection, we strongly advise you to consider using a more complex antivirus solution."
Look at avast! click here AVG click here or Antivir click here All offer better protection.