Hiya,
You are perfectly safe on the daily boat trips in the Bodrum area. You don't have to swim anywhere - the boats stop at 4 or 5 bays during the day, for people to swim, but if you get a trip that goes to Camel Beach, you actually moor up at the jetty there, and can walk from the boat onto the beach, to have a drink, ice cream etc.
You shouldn't feel seasick either - I suffer from travel sickness, including on ferries, but I've never felt ill on a boat trip in Bodrum (and I've been on loads of them).
Its a great value day out, and there is absolutely no better way of topping up your suntan. Just remember to put on loads of suncream, often, as you don't feel the sun burning so much on a boat, as there is always a breeze.
Happy holidays,
Elaine