Looking at my WDW road map I would say you will arrive faster if you turn left on Victory Way [ it is the road to Pops Century & Art of Animation] and then right on Osceola Parkway.
Osceola Parkway is a straight shot to the Animal Kingdom. I think you will miss 2 or 3 lights compared to driving around on Buena Vista Drive then finally turning right to go up the slope to catch Osceola Parkway.
If you are at Animal Kingdom at rope drop and you don't stop to do anything but walk straight to the Safari you should not have to wait at all as all the trucks start out empty so they can accommodate a lot of people the very first thing in the morning.
By the way - you will turn right after the guard shack at Bonnet creek and then turn left at the light on Buena Vista Drive. The first light will be Caribbean Beach Resort. The second light is Victory Way so you will need to get into the left turn lane. My map is old and shows no lights on Victory Way but the map is from before there were two resorts on this road so there may be a light for Pops Century and a second light for AofA. Otherwise the first light will be Osceola Parkway.