From the root - beber - which means to drink in Spanish. Adding the "se" makes the verb reflexive, hence making the word "to drink oneself."
This had also been proven - sticking a straw in a resevoir of saliva in the side of your mouth, sticking the other end of the straw in the middle of your mouth, and sipping the latter will result in the drinking of your own saliva.
Trying to fend off dehydration, James se bebe saliva.
Note: Here, the verb is conjugated.