"to soil or wet by dragging in dirt or mud or from being rained upon," 1727, from be- + draggle "to drag or draw along damp ground or mud." Also in a similar sense were bedrabble (mid-15c.), bedaggle (1570s).
bedlam
Bedlamite
Bedouin
bedpan
bedpost
bedraggle
bedraggled
bed-rest
bedridden
bedrock
bed-roll