To cover something with saliva or drool, or to make something messy with dripping liquid.
From 'be-' prefix combined with 'drivel' (from Middle English, possibly from Old Norse 'drífa' meaning to drift or drip). The prefix intensifies the action.
Bedrivel is one of those marvelous medical-adjacent words that probably originated in nurseries and sickrooms, where drooling and dribbling were constant realities people needed to discuss without embarrassment.
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