of bud-the act or process of producing buds.-a process of asexual reproduction, in which a new organism or cell is formed by a protrusion of a portion of the animal or vegetable organism, the bud thus formed sometimes remaining attached to the parent stalk or cell, at other times becoming free; gemmation. see hydroidea.-the act or process of ingrafting one kind of plant upon another stock by inserting a bud under the bark.