A component on a composite bridge plug used for plugging a wellbore includes a first member including a wound composite material, and a second member including a molded fiber phenolic composite material. The wound composite material of the first member makes up more than half of a volume of the component. The first member is a convolute-wound core having a cylindrical shape. The second member forms an outer shell that is molded over an outer surface of the first member. The component is a cone of the composite bridge plug.