Would also recommend to consider MO Bodrum.

Stayed there five years ago and it was great. A lot of attention to details, great restaurant menus, good location and spacious & modern rooms.

If it’s more for privacy and good beach, Six Senses might work much better, but a few mentioned here already, the place is a bit further away.

Cannot comment on the Edition, but just from pictures and location it doesn’t look too appealing for a relaxing holiday.