Rather than attempt to make our own way we did do an organised coach tour from Marmaris to Olu Deniz a few years ago.
We were told we would be picked up by coach from our apartment but the bus was quite late in coming for us (no surprise there really!) We then went round Marmaris to many other hotels picking up others before we started our journey. The trip included a stop somewhere for lunch and a swim (1 and a half hours). I do remember we had a bit of a trek, in all the heat, from leaving the coach to getting to the bit of the beach that we settled.
Truthfully we found it a bit disappointing as we had very little time to relax and spend at the Lagoon. Came back in the evening shattered! An overnight stay would be a good idea.