Get a hypodermic syringe and needle, I use the green ones that are about 50mm long, the shorter, heroin addict ones are too narrow to allow the glue easily through, and inject the PVA glue into the space between the layers. The bat has probably opened up quite well so it is easy to get the needle into the cavity. Depending on the size of the de-lamination you may need to inject a number of areas. Clamp hard and use a scrap piece of material to spread the pressure across the repair and to protect your bat.
Good luck.