bath caulking

About a year into a new bathroom, the silicone started peeling away from the bath and getting mouldy. It gradually detached along most of the length of the bath. I've put this off for a while but now decided to try and tackle this myself. The bath is Carronite (acrylic) so I wondered if maybe...

I was wondering how to go about caulking this particular bath, that has a rounded wood placed between the tiles and bath and come out with one flush finish? Picture attached, I am a complete newbie when it comes to caulking but have a good idea of the basics. Any advice would be greatly...