As a Tiger Den Leader, I think it is great to be able to work and earn the Bobcat Badge at the beginning of the Tiger year, and with solid parental involvement, the oys can easily complete the requirements. It sure is challenging for the little guys to explain the meaning and parts of the Cub Scout Promise and the Law of the Pack required for Bobcat, but the boys are certainly able to memorize and repeat the law and promise purely through repition (and adult partner home practice) during the opening and closing of each meeting. We started memorizing and discussing the law, promise, motto, hand shake and salute (all Bobcat requirements) in August, and the Tiger Den is right on track to receive their Bobcat Badge in May.
Both the 2005 Tiger Handbook on page 152 and the 2005 Cub Leader Handbook on pages 19-6 & 19-7 state that Tigers can indeed earn their Bobcat after they earn their Tiger Badge and while still Tigers. There is no requirement to wait until June 1st.