When I lived in BoD and worked in Altens, I always used to go through Ferryhill, cross the bridge by the bottom of the Duthie Park and up the Tullos Ring Road. Rarely took more than half an hour door to door, even when they were digging up Market Street. I think there's a shortcut through Kincorth that takes you out by the police station too. You could probably take a right after the bridge and take the A90 too if you wanted, I did that a couple of times when there was a big queue to turn left. If the white elephant bypass is ever built, there will be that option too.
Regarding the bus going up Wellington Road, I'd assume someone somewhere would have some common sense and have a dedicated bus lane somewhere, perhaps going between Kincorth and the stadium, similar to the lane that goes from Lang Stracht to Kingswells Park & Ride for buses only. Would encourage more people to leave the car too.