I think it took me less than ten minutes, but I was alone and had no one who might want to stop to go to the bathroom, get a drink, grab a picture, etc.
I took the bridge behind FOTLK, but I understand in super heavy crowd times, it is designated as an exit from Pandora only and you cannot enter from there.
The bridge was open as an entrance on July 1st, 2nd, and 6th for sure. It is the quicker way from KS.
As a precaution, I always give myself at least twice as long as I think I will need. Also keep in mind that the Safari can take a long time, too. It once took us over 45 minutes from entering the fastpass line to getting off the safari. Sometimes animals block the truck paths. Sometimes they aren't running as many trucks. It is better not to feel pressed for time. That can really mess up your enjoyment of the safari if you can't enjoy the beautiful giraffes walking in front of the truck when all you are thinking is, "I've got to hurry to catch that next fastpass."