What if you combined the 2 suggested? You could put the 4X4 up with a brace underneath, take a skill or jig saw whack the bottom off the bucket, slide it over the 4X4 and screw it to it.
You wouldn't have to worry about time, saddle weight, and dropping it in a hurry tearing a hole in your saddle lining using both. You'd still have the storage cubby. If it were me I'd drill some holes in the bucket to discourage mold growing underneath the actual saddle resting area of the bucket.
An added bonus would be spring cleaning, remove a couple screws, take down the bucket, blow out the tack room, hose off the bucket, air dry, replace the bucket back on the rack.
You still can't beat one made into a triangle of 2- 1X6's on the sides and 1- 2X8 in the middle braced with a piece of scrap or shelf bracket underneath.
"Light travels faster than sound. That's why some people appear bright until you hear them speak."
Larry the Cable Guy