No, it is not free. Antivirus that wants to use their database have to contact them to strike a deal, where the will receive Bitdefender SDK with updates available. To get more info you will need to contact Bitdefender directly, as the deals are all made with a Non Disclosure Agreement, hence the lack of info to public.
Getting a SDK licence from BD will cost around 5000 Dollars for just the SDK. If you want the whole package full support, updates and full re-branding it will cost 4 times as much. I know this for a fact as one of our clients has such a licence.
And BD is pretty expensive yet its one of the better ones, as some others start with around 1000 dollar SDK bronze partner fee.
But in the end no matter what brand you are going to take if you want to do it properly you are looking anywhere between 2000 dollars up to 20k