you cant fly between the two, they are only about 80 miles apart.

there are buses bewteen the two cities (you may have to change in Aydin on some of the routes)

i hired a car and drove from bidrum to ephesus past kusadasi izmir, if you drive the road was good ,nice scenery,took about two and half hours, well signposted,cant remember how long it took to izmir but pretty fast road to ephesus way beyond izmir