in reference to jazz, "earthy," by 1929, supposedly originally a reference to the buckets which caught the drippings, or gutterings, from barrels. Which would connect it to gutter (v.).
Entries linking to gut-bucket
gutter v.
late 14c., "to make or run in channels" (transitive), from gutter (n.). Intransitive use, in reference to candles (1706) it is from the channel that forms as the molten wax flows off. Related: Guttered; guttering.