If the strip of plastic seems to be fixed behind the tiles, its quite a problem to fix as the only proper way is to remove the tiles and replace the trim....however, as you have bought some silicone bath sealant, squeeze a good layer between the bath and the tiles, and press it in with your finger and it should seal quite well - get rid of any excess before it dries and make sure there is no dampness before you start.
Boy John
April 2008