hmmm.... yeah, that's not a bad option.
For this one, I would rack to secondary, clean the bucket, add priming sugar solution to the bucket, rack back to your... bottling bucket..., bottle, then go get an actual primary carboy or bucket
BTW just so you know, a glass carboy with ribs around the sides is too small to ferment a 5 gallon batch. A primary glass carboy is smooth around the sides and holds around 7+ gallons. A Primary bucket is also 7+ gallons. Bottling buckets are generally a little smaller in diameter and really only hold around 6 gallons... which isn't big enough for fermenting if you get yeast that really kick off. It'll krausen right out the top and make a mess.