Well off the top of my head at a guess (you have an electric shower) what you've got is hot and a cold to the bath and then a cold to the shower (whoever fitted it took the feed nearer to the main).
Go the shops and buy some masking tape, a silicone gun (you don't need alicence) some silicone and maybe a stanley knife, or some silicone sofener and maybe a wonderbra! I think you're being modest. Silicone can be a swine to rake out but once done, put your masking tape on the bath and on the tiles as close to the join with the wall as you can (not too close), go over it with your silicone, then rub your finger along it to flatten it out, if you see any gaps go over it again, pull away the masking tape (whilst it's still wet) check for any gaps and then leave to dry for 24 hours. Try it the whole lot (wonderbra excluded) will come to no more than �15 �20, worth a pop.