It seems there is a long-standing problem that foreign tourists visiting Goreme for the first time tend to be dropped off prematurely at Nevsehir bus station, although their ticket stated clearly that their final destination should be Goreme...
To be honest, it is not easy to tell when you board the bus in Istanbul or Ankara whether the bus will stop at Goreme station en route to Nevsehir, or it really by-passes Goreme and go directly to Nevsehir.
It is probably easier if one simply buys a ticket from Istanbul or Ankara to Kayseri instead, then change bus at Kayseri's huge bus station to Goreme. In this case, there is no danger of one being dumped at Nevsehir because the Istanbul-Kayseri or Ankara-Kayseri buses DO NOT go via Nevsehir. Hence you can be sure you won't be dropped off prematurely.
However, if one insists on taking one of those so-called 'direct' buses serving Istanbul/Ankara - Goreme, and finds himself indeed being told to get off at Nevsehir, be calm. There are a few possibilities:
1. The so-called 'direct' bus is actually not a direct service at all, but all passengers - Turkish or foreign - are required to get off at Nevsehir and change to a free shuttle service (so-called service bus, usually operated by the same bus comapny using mini-vans). If everybody (including all Turkish passengers) gets off the big bus, observe their movements. Normally 2 or 3 small vans operating the free shuttle service will appear almost immediately. One of those mini-vans heads to Urgup, another to Goreme. Ask which one goes to Urgup and which one goes to Goreme. These shuttle services are free and there is no need to pay anything extra for the bus.
2. If there are still passengers remaining on the bus, you can reasonably suspect that Nevsehir is not the final destination of this bus.
See the white mini vans in the photo? These are the free shuttle service that ferry passengers from Nevsehir bus station to Urgup and Goreme.
For those of you who have never been to either Goreme or Nevsehir before, but holds a ticket which stated that your final destination is Goreme, it is important to know how Nevsehir's bus station looks like, in case you are told by bus driver and attendant to get off prematurely at Nevsehir:
Front view of Nevsehir's bus station (Otogar/Terminali). If you are supposed to go to Goreme on a 'direct' bus, this place is not your final destination.