I'm inclined to agree that when the recovery team reported "bucket" they meant bucket and not a bin, unless the container was so melted they could not determine which.
I did find a "Little Giant 20 qt (5 gallon) Bucket in green sold by Ace Hardware. At 10:47AM, AxC's phone pinged in St. Anthony and there is a Dan's Ace Hardware store in St. Anthony. I checked online and the bucket is not currently available in-store there, but can be ordered and picked up in-store a week or so after order.
But, maybe that bucket WAS in their inventory on Sept 9, the day AxC went into St. Anthony. It is currently in inventory in the Dan's Ace Hardware in Driggs.
Little Giant 20 qt. Bucket Green - Ace Hardware
IMO, TR's body was not likely dismembered before delivery to CD's property, but instead disjoined as it was removed from the fire pit after burning was attempted. This likely accounts for finding some uncharred pink flesh, which would likely be at the points were disjoining occurred and uncharred flesh became exposed.
If AxC and CD decided to "cancel" the burn the body to ash plan after an hour or so and opted for burial instead, they may have used tools (shovels, rakes) to - as quickly as they could - drag the hot parts from the fire pit to the burial site (behind the end of the barn out of view of the house and back driveway) and then decided they needed a container to gather some of the many hot smaller parts to move all at once. So, AxC headed into nearby St. Anthony for a bucket while CD, the graveyard sexton began digging.