hi,
we did that once in April. There is only 1 boat at 09:30 to Kos Town, in winter maybe not every day, see the schedule http://www.bodrumferibot.com/en/calendar.asp or
http://www.bodrumexpresslines.com/timetable.php. You can send them emails and and at least I got a response. The price was 12€ in April. There is no direct connection to Kalymnos. All the border formalities are done at the harbour, also your luggage gets checked or scanned (depending on the size).
From Kos Town there is not many boats to Kalymnos so you probably have to go to Mastihari. In Kos Town there is not many buses to Mastihari, so you might have to catch a taxi to Mastihari which cost us 28€ in April. In Mastihari you catch the ferry to Kalymnos. So we arrived in Kalymnos early afternoon.
Arriving in Bodrum from an origin outside of Turkey and coming out of the plane you have to enter the bus for international transfers as they have 2 different terminals depending on where the people come from.
We stayed at Hotel Gulec http://www.hotelgulec.com or boking.com, which is not far from the harbour, you could even walk. Rooms are small but clean, rate was somewhere between 30 and 35€ for a double room. We organized a pickup at airport with this Hotel which worked quite good and because we arrived in the late evening we were happy about it, this airport was not very busy. This pickup was around 45€ which is the normal taxi price.
You can also find cheaper pensions and food is also very cheap. Bodrum is a nice little and relaxed town.
So it is a long journey via Bodrum, but it is quite relaxed and as flights to Bodrum are cheap we might do that again. If you come via Athens it might be not shorter.
cheers, Claudia