We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a three-dimensional topological insulator (TI), coupled by the proximity effect. The magnetic texture of skyrmions can lead to confinement of Dirac states at the skyrmion radius, where out-of-plane magnetization vanishes. This confinement can result in charging of the skyrmion texture. The presence of bound states is robust in an external magnetic field, which is needed to stabilize skyrmions. It is expected that, for relevant experimental parameters, skyrmions will have a few bound states that can be tuned using an external magnetic field. We argue that these charged skyrmions can be manipulated directly by an electric field, with skyrmion mobility proportional to the number of bound states at the skyrmion radius. Coupling skyrmionic thin films to a TI surface can provide a more direct and efficient way of controlling skyrmion motion in insulating materials. This provides a different dimension in the study of skyrmion manipulation.