Instead of using the bolts and nuts you already are using to hold the bucket on, run the light through the same hole and put a nut on the inside of the bucket. Make sure your ground wires are attached.
I used a pair of lights distributed Lockhart Phillips and they fit the existing nuts inside the bucket so it was a dead simple bolt on. Most of the bullet lights seem to come from the same place (don't know the brand) and I bet your's will be the same.