I am assuming you are fermenting in the bucket, then transferring to secondary for a period of time. Assuming that, the bucket would then be cleaned out, and then sanitized at the time of bottling. When you transfer from secondary back to the bucket, I would just put in your boiled corn sugar in the bottom first. Then transfer your beer into the bucket and bottle as you mentioned. Since you left behind most of the yeast the first time and whatever settled in the secondary as well, your sediment in your bottles should be pretty minimal.
The only thing that is easier with a bottling bucket is you don't have to start the siphon, then keep it from spilling all over the place while you get the bottling wand onto the end of the hose. You can use a turkey baster to start a siphon easy enough.
I recently made a 1-gallon test batch of my Pale Ale, and after transferring it to a 2nd 1 gallon jug, I just bottled the few bottles straight from there with a hose and bottling wand. Worked easy enough. If money is an issue for you, I'd just bottle with the primary bucket.