We've just returned from Kos (Tingaki) and done the Turkey day trip on a Tuesday (market day)
We booked this through Theokratos travel on Tingaki main street, who arranged everything for us.
There was a 3 euro tax to pay (inc. in ticket price) plus a further 1 euro 'port' tax to pay in Kos town.
We took up the optional free 1 hr town tour in Bodrum - which was interesting and dropped you off near the covered market, it stopped at some disused windmills (nice views of harbour) and stopped [briefly, on roadside] outside the ampitheatre(got a couple of photos, which by the looks of it was all that was needed!) - tour was funded by Bodrum Gold Centre, so there is a visit to their sales room as part of the tour.
We done the market, had lunch, then walked down to the Castle - unfortunately we didnt leave enough time to see all of the castle (it's big!) before having to catch hydrofoil back. You will need at least an hour or two to go around castle properly.
Entry to castle is in Turkish Lira only (10YTL each) We only had 30YTL and having 'ran' back through the Turkish streets in 40 degree heat to get 20 more Lira, the lady at entrance told me that the 3 children could enter on the one ticket ! (the 20+ extra Lira came in useful for Duty free's though as I could use both currencies at once)