Someone who isn't AS drunk as the person throwing up into a bucket, garbage can, sink, toilet, etc. The Bucket Coach is usually drunk, and thus willing to help their comrades with their 'ordeal'.
They can either be yelling words of encouragement, holding the bucket, holding the person puking, or a combination of these.
Bucket Coach: "COME ON puke out that fireball like a motherfucking DRAGON!!!" *Slaps puker on the back*
Puker: *BLAAAAAGHRGGHHGRGHHH* "I feel...be.." *BLAAAAHGGGRRGHH*