I have to say, imbibe is a surprisingly interesting word. Yes, I’m aware of how crazy that sounds, but come see what I mean.
Imbibe showed up in the late fourteenth century, and like most words, it comes from Old French and classical Latin. In French it was imbiber/embiber, which meant soak into, and in Latin it was imbibere, where it meant assimilation or absorb. Although we never drop the prefix in English, bibere is an actual word in Latin meaning drink, and the im- comes from in-, which means into. And it might not seem like it, but bibere is also related to another Latin word for drink, potare, the origin word for potion. Potare can be traced back all the way to the Proto Indo European po, also to drink, meaning it went from drink to mentally absorb (“drink inward” in a figurative sense) and then back to drink as it moved through the centuries.
The cool thing about imbibe is how it’s related to other words—like beverage. Beverage comes from the Anglo French beverage (if you can wrap your head around that radical spelling), and before that the Old French bevrage, which is the basically another Old French word, boivre, with the suffix -age stuck on. And where does boivre come from? The classical Latin bibere, of course.
There’s also bib, which actually kind of makes sense when you think of the “absorb” definition. It showed up in the late sixteenth century, coming from the word bibben, which apparently was a real English word once upon a time. Although crazily enough, people aren’t one hundred percent sure that bib (and bibben) are really from bibere.
That’s not all, but there’s less certainty about the other words bibere might be related to. Imbue is a possible relative, which makes sense since it means to saturate or cause to absorb. It can be traced to the Latin imbuere, same meaning, but there’s no actual evidence it’s related to bibere. Beer might also be related, coming from the Old English beor, but it’s origin beyond that is “disputed” (i.e. they’re even less sure about it than usual). Still, the theory is there that the German originator of the word (of course it’s German; what did you expect?) took it from the Vulgar Latin word biber, which meant a drink, and you know it’s related to bibere.
TL;DR: Tons of words might be related to imbibe. They also might not be. Language!
Tony Jebson’s page on the Origins of Old English