Driving is about 15 minutes John, you couldn't walk it unless you are barking and want sunstroke/dehydration/death. I'm not sure on taxi prices anymore but if you are in Fethiye or get to the Dalaman road, the bus (dolmus) service is every 10 minutes and drops off/picks up at the Majesty Hotel gate.
It's a lovely hotel, we stayed there for a long weekend when we lived over there.