Composite parts such as plastic laminates are formed using a pre-assembled, integral double bag to vacuum bag the part. The double bag is formed of two sheets of bag material that are cut to pre-determined width dimensions, with the width of one sheet being less than that of the other. The bag sheets are prealigned and then attached to each other by spaced apart bonds between the sheets which hold the bag sheets in registered relationship to each other when the double bag is placed over the part and sealed to a tool base. The attachment bonds may be formed by ultrasonic welding, heat sealing or an adhesive.