A bucket for crushing inert material comprises an outer casing, an inlet section for the entry of the material to be crushed into the casing and crushing unit arranged in the casing for crushing the material and a screening device for screening the material to be crushed disposed in a position intermediate between the inlet aperture and the crushing unit. The screening device comprises at least one rotating member, the partial rotation of which is suitable for performing a screening of parts of material to be crushed which are of a size below a predetermined dimension.