G stumbles alongside Ugetsu, paying little mind to his surroundings as they walk along, "I'm gonna 'tend t'it, jus' goin' to do it o'er a bucket."

Because he is convinced he is a manly man, and manly men don't accept help. They puke into buckets and embrace the full effects of their hangover with pride! Either that or G is just being a stubborn drunk who will regret this way of thinking tomorrow when his existence is reduced to a headache with legs.