Your sugar probably isn't going to mixed well. You may a have a few bottles that don't carb well.
It's best to dissolve the sugar into warm water and let it cool. Then put that into the bucket and siphon on top. I know you knew that, but if you forget you can always add the water sugar to the beer and gently stir it in. It's no biggie so long as you don't splash it around while stirring.
Do you have an auto-siphon? If you do you can stick the siphon in the beer and stick the tube down as low into the beer as you can get it. Start the siphon and lift it up to the top where the priming sugar is most concentrated. It will basically circulate the liquid in the bucket without adding oxygen