When I bottled, I added my priming solution to the bucket hot and racked beer onto it, which did good job of stirring it in. As far as to O2 pickup, it is not a problem with bottle-conditioned beer, as the yeast will rapidly consume any O2 that gets absorbed because they have to go through the fermentation process a second time. Unlike kegged or force carbonated bottled beer, bottle conditioned beer has a new carbon source to deplete. That is one of the benefits of priming in the bottle.