Great idea Holly! I never would have thought of using an ice bucket for a little kitchen compost holder but what an economical idea; and as you stated, they can usually be found in thrift stores ... or sometimes hidden away in a kitchen cabinet.
This brings back memories of my dear mother in law who alway kept a plastic container with a tight fitting lid by her kitchen sink where she'd place things for the compost pile; she also used to bury some food scraps right in the garden.