In this paper we study some properties, namely Global Generation and Strong Normal Presentation, of specific types of (twists of) Picard bundles over the Jacobian of a curve. Our main tool is the notion of M-regularity introduced by G. Pareschi and M.Popa.In this paper we study some properties, namely Global Generation andStrong Normal Presentation, of specific types of (twists of) Picard bundles over the Jacobian of a curve. Our main tool is the notion of M-regularity introduced by G. Pareschi and M.Popa