Esenboga has bus links to the center, both city bus and airport bus. Not sure = I doubt that they will drop you off next to the hotel so you might need a short taxi ride which wont be too expensive.
Did you check with the hotel whether they have a service and what it would cost. This might be a good option given that the bus ride is slow.
ADD-ON: Just saw that you made a double posting. I m sure the friendly board member from Ankara will provide you with more precise and up-to-date info. :)Edited: 22 June 2017, 14:33
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