Yes this is the bus that runs via Basko. The Winter timetable last year was only 2 buses a day:
From Lakeside/FCC/Turquoise: 0910 and 1010
From Bodrum: 1200 and 1700
The service increases in April to 3 a day and then in June to 6 a day before the summer timetable comes into force at the start of July.
I wish the bodrum shuttle would be the same price as the dolmus as it would have been packed over the summer - they quoted me 20 lira to take me to guvernlik (sorry for spelling)
Güvercınlık.