"Bebe" is the second person imperative, informal, of "beber." You are asking your friend "Drink more water, please." There are other imperative forms for Usted, ustedes, don't drink, and so on. "Bebe" is the same as "he/she/it drinks," so you need to take the cue of "por favor" to see it is an imperative. Not easy to understand the first time ... or the next ...
Both answers are correct, even though DL does not mark them. Just with "por favor". In fact all of the following answers must be correct for the English imperative "Drink":
Imperative, 2nd person of "beber":
bebed (vosotros or vosotras)
Bebe más agua, por favor informal, addressed to one person.
Beba más agua, por favor formal, addressed to one person.
Bebé más agua, por favor voseo, addressed to one person.
Bebed más agua, por favor informal, addressed to more than one person.
Beban más agua, por favor formal, addressed to more than one person.