First thing is to position your 2 x 6 perpendicular to the handle (see Starboard and Port Bucket build 1 of 3.). In other words make sure the handle is directly above the end-grain of the 2 x 6.
Using 1" or 1+1/2" Sheetrock screws, put a washer under the head of each screw and attach the Bucket to the 2 x 6 (screws and washers are positioned inside of the Bucket going into the 2 x 6) with four screws. Locate the screws ~ 1" inboard from the walls of the Bucket, 3" from each other and centered on the 2 x 6.