It's very easy to get a bus from Bodrum to
Marmaris and very cheap. Round about £8 last year if I remember rightly. Just go to the bus station and anyone there will show you where to get tickets and make sure you get on the right bus. It takes about 3.5 hours. The buses are very clean and comfortable and you get free drinks and snacks en route. I don't know about taxis as never use them.