Summary

Simple lint roller.
Print, assemble, put double sided tape on the barrel.
Then put masking tape, non sticky side down onto the barrel.
Hey Presto!
When full of bits, simply peel the masking tape off and replace.

Printed at 0.2, PLA, 10% infill with supports.

EDIT... Use masking tape (painters tape) as opposed to normal sellotape or gaffer tape. This way, the double sided tape will last.