You can take shuttle from Milas airport to Bodrum Coach Station and from there you can take Gumusluk local buses (app. 60 min.) or you can go to Yali Mevkii by taxi (app. 40 min.)
Generally, bus companies have Turgutreis service. (You should ask it.) If you go to Turgutreis, you can take Gumusluk local buses (dolmush) and arrive to Yali Mevkii in 25-30 minutes.
There are minibuses from Bodrum to Gumusluk, from Gümüşlük to Bodrum every 15-20 minutes, for 24 hours during summer. The route is Bodrum, Gumbet Kavsagi, Konacik, Bitez Kavsagi, Ortakent, Yahsi, Gurece, Derekoy, Peksimet, Karakaya Village and Gumusluk Yali Mevkii.
There are minibuses from Turgutreis to Gumusluk, from Gumusluk to Turgutreis every 15-20 minutes, for 24 hours during summer. The route is Turgutreis, Kadikalesi and Gumusluk Yali Mevkii.
Turgutreis minibuses follows this route: Kadikalesi, Gumusluk, Cukurbuk, Koyunbaba, Gumuskaya, Geris, Yalikavak, Gundogan, Turkbuku and Golkoy.