Based upon what you said, namely that you only have the one container and it is currently filled with your cider, here are what I see for the pros/cons:
Adding it directly to the bucket will give you a consistent carbonation because, as has been mentioned, you can make sure it is uniformly mixed. The downside to this is that you'll stir up the junk that is at the bottom of the bucket too, which you can end up putting into your bottles. If you go this route, I would gently stir the sugar solution in, then I would let it sit for an hour or two before bottling to let the sediment fall back to the bottom.
Adding sugar directly to the bottle is perfectly fine, but it is pretty tedious. If you go this route, use a scale if you have one to be consistent in how much you put in each bottle.
Another option that you might have available is if you have a big pot, you can bottle in batches. If your pot holds a gallon and you have five gallons of cider, then split up your sugar in five portions and do it that way.
If this is the first time you've ever bottled, make sure you are confident that your cider is done fermenting. An early mistake is to rush your product into the bottle and find that it keeps fermenting in the bottle and you end up with bottle grenades.