Hi there, I am afraid I cannot be of much help on buses as we tend to drive everywhere.
I do know there is a bus that goes past Miletos as there is a lady that lives in Balat village which is near to there & she uses this to come into Altinkum every week.
Miletos is one of my favourite places in the area & well worth a visit, but if you could hire a car for the day, you could continue on to Doganbey for a lovely fish lunch & then to another ruin called Prienne.
From Tuntas Suites, it is an easy walk into Altinkum & there are dolmuses at the bottom of the boulevard which will take you up to the Apollo Temple which has some lovely Turkish Restaurants. It is not that far to walk, but it is up hill, so if anything I would recommend walking back down to town rather than up to the temple.
From Tuntas there is a coastal path which you can follow around through Yesilkent & Fevsipasa which have some lovely quite beaches & pontoons to sunbathe on. I believe this path can be followed all the way to Akbuk, but I am afraid I cannot say this with any certainty as I have not managed to walk that far!!
Lake Bafa is lovely too & there is an ancient Greek Village on the other side of the lake. A number of tour companies do trips here from Altinkum, but I guess it could be possible to get the Bodrum bus & ask to dismount at the lake.
One of the members of this group has compiled a website with lots of useful information If you would like to take a look - http://didim.me/bus-routes/bus-routes
Hope you have a great holiday & enjoy your time in our lovely town.