As heard in some George Roberts solos, a bucket mute can suit the bass trombone very well. Apart from possible bell size differences, this what he used.
It needs careful handling for two reasons. It's very easy to add little dents to your bell if you don't make sure all 4 grippers are outside the bell as you push it on. This is therefore NOT a great design for 2-bar mute changes, though most composers/arrangers seem to understand this. The cotton wool inside is held in by what seems to be glued-on cheesecloth so it's much more delicate than your cup, straight and plunger.