When I get the priming sugar ready to bottle, do I put it right in the bottling bucket after it boils for 5 minutes or do I let it cool to room temp before I put it in?
You can put it right in the bucket and rack onto/into the solution. The small volume of priming solution is going to cool pretty quick just from hitting the bucket and the beer will be fine. Pouring it in while hot will help keep it from picking up any unwanted bugs.
Well I'm glad someone else said 'go hot.' I usually do and haven't had problems, but all the info I've read on this topic says to boil, cover and cool just like you would your wort.