Marmaris is a large resort. It depends on what part of the town you are staying as to where you can hire a bike, but most parts will have a cycle hire shop of some description. The roads are a different matter altogether. Other than in April when there is the Tour of Turkey cycle race held along the roads of Marmaris, I can’t say I have ever seen a bike on a road there, neither would I like to try it. There would be some good mountain routes up through Icmeler and heading for Turunc. But again, these are busy roads and might be a little dangerous with the other road users traveling a little too fast. There is a good coast path from Marmaris into Icmeler and this is probably about 5-6miles end to end. This is mostly a flat route though and might not be very testing for you. Alternatively, it’s a good running path if you fancy a change.
Here are two bike route map sites