Since I'm using Cooper's fermenters with the built in spigot I bottle directly from them and add the priming sugar to the primary. I do just like you asked, a gentle stir around 2-3 times then bottle. I've bottled by racking to a bottling bucket as well when I first started using priming sugar (used to use carb drops). Never noticed a difference between racking to a bucket or doing the sugar in primary and bottling from there.
A few weeks ago I bottled 2 brews the same day. For the sake of finalizing my curiosity I bottled one by doing the usual priming sugar into bottling bucket and racking into it. The other beer I added the priming sugar directly to the primary, gently stirred making sure not to disturb the bottom sediment, and bottled straight from the primary spigot. I popped up a few bottles of each over the past few days and both are perfectly carbed, perfectly consistent, and no additional sediment in the one I bottled from the primary.
So from now on I'll always be adding the sugar to my primary and bottling straight from the built in spigot. For one, it's super convenient. Additionally it's a little less cleanup not having to wash a bottling bucket. Oh, and for the record I don't do Cooper's kits or anything like that, I brew AG and prior brewed with extract.
Rev.