I always thought "dust my broom" meant to leave, as in Robert Johnson's "I Believe I'll Dust My Broom"

I'm gon' get up in the mornin' I believe I'll dust my broom
I'm gon' get up in the mornin' I believe I'll dust my broom
Girl friend, the black man you been lovin' girlfriend, can get my room

A rider is a sexual partner.

According to the notes in "Robert Johnson The Complete Recordings," "A nation sack is a small pouch worn around the neck in which keepsakes and valuables are kept."