There is no direct counterpart that is in typical usage. Use any word that suggests desperation or urgency, if you must use an adverb. Describing the way the person drank visually would probably be more far more descriptive, however. For example: The traveler sank to her knees, grabbed the jug with both hands, drank the entire contents in one messy draft.
"The traveler sank to her knees, grabbed the jug with both hands, drank the entire contents in one messy draft."
Actually, I would like to add that ravenousravenous is not necessarily a term just for hunger; a ravenous thirsta ravenous thirst is a perfectly acceptable phrase. Ravenously Ravenously also means greedily or in a predatory manner; it is literally derived from the word ravenraven (like the bird). Thanks OED.