Of course, you can... but I would recommend, if you can afford it, to buy a second carboy for secondary. Then, rack to the bucket for bottling. Yes, it's one more step, but it makes for less sediment in the bottles.
Also, maybe you don't want to secondary it in a bucket with a spigot? I may be entirely wrong, but will that have some kind of negative effect on the seal of the spigot?
Also- how much head space will you have once you put it in the secondary? Too much air is bad for brew.