Let C be a smooth curve, and M (r) (C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We examine the generalized Verschiebung map V-r : M-r(C-(p)) -> M-r(C) induced by pulling back under Frobenius. Our main result is a computation of the degree of V (2) for a general C of genus 2, in characteristic p > 2. We also give several general background results on the Verschiebung in an appendix.