The invention is directed to a nonwoven material made of a bicomponent fiber in which the first polymer is a cellulose ester polymer, preferably cellulose acetate, and the second polymer is selected from the group consisting of polyolefins, polyesters, polyamides and polyimides. The bicomponent fiber can be either a side-by-side or a core-and-sheath fibers. When core-and-sheath, the cellulose acetate is the sheath polymer. The nonwoven material of the invention can be used to prepare grips, materials for use in absorbent products such as diapers and personal hygiene products, disposable towels and other products. The nonwoven of the invention has particular utility for disposable diaper products due to the superior fluid acquisition, retention and distribution properties of the cellulose ester, yet avoids the high cost of all cellulose acetate fibers by use of a much less expensive second polymer to form part the bicomponent fiber.