mixing sugar with the beer..

I am going to bottle my beer tomorrow, so i have a question about carbonation.

When i have added the sugarwater in the bottling bucket, and i have used the siphon with a flexi hose and layed the flexi hose in a cirkle to mix the beer and sugarwater in the bottling bucket.
Do i stir the beer gently with the siphon to mix the priming sugar and beer propably, or is it enough to just have the flexi hose in a circle in the bottling bucket?

The reason i ask is because i am little worry about getting to much air in my beer..

stir at the outset to mix the sugar, then stir again half way through.

I have personally never stirred while I bottled. I just made sure that the beer was flowing in with a circular motion. I have never had and carbonation differences within batches

I don't stir either and get consistent carbonation.