"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).
word-forming element of verbs and nouns from verbs, with a wide range of meaning: "about, around; thoroughly, completely; to make, cause, seem; to provide with; at, on, to, for;" from Old English be- "about, around, on all sides" (the unstressed form of bi "by;" see by (prep.)). The form has remained by- in stressed positions and in some more modern formations (bylaw, bygones, bystander).
The Old English prefix also was used to make transitive verbs and as a privative prefix (as in behead). The sense "on all sides, all about" naturally grew to include intensive uses (as in bespatter "spatter about," therefore "spatter very much," besprinkle, etc.). Be- also can be causative, or have just about any sense required. The prefix was productive 16c.-17c. in forming useful words, many of which have not survived, such as bethwack "to thrash soundly" (1550s) and betongue "to assail in speech, to scold" (1630s).
"to wet or befoul a garment by allowing it to drag along damp ground or mud," 1510s, frequentative of drag (v.); also see -el (3). This led to draggle-tail "sloppy woman, woman whose skirts are wet and draggled" (1590s). Related: Draggled; draggling.