Shell Busey talks about a silicone and adhesive remover that you can use to remove the silicone around your bathtub.
He also tells you how to properly re-caulk the tub after the old silicone has been removed.
This Silicone and Adhesive Remover is designed to break the bond between the silicone and the surface it is applied to. Spray the Remover along side the silicone and work it under the silicone with a plastic or metal scraper. This product also removes any other unwanted adhesives by spraying the surface and wiping it away.