The phrase "ice cream bucket" refers to a container that holds ice cream. It's simply a bucket or tub used to store and serve ice cream. Full definition
I tried storing it in a number of different ways from leaving it in the toilet, to sitting it in an old ice cream bucket. (clothdiapergeek.com)
We don't cloth diaper, so I used an empty ice cream bucket as a wet pail for the wipes. (thefrugalgirls.com)
If you like Ben and Jerry's Chunky Monkey ice cream — I'm sure you're gonna love these brownie bars, that are some king of homage to the popular ice cream bucket. (lilcookie.com)