Register lies on bed wrapped in petition (9)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

[ BS(abbrev. for “bullshit”/lies/untrue talk or writing) plus ( on ) CRIB(a child’s bed/cot) ] contained in ( wrapped in ) SUE(to petition/to ask formally for something). Defn: …/to enlist to be a participant.