I would love any information on advice on taking a night bus from Cappadocia to Pamukkale. It would reduce the amount of backtracking and really help the budget but it might also be miserable because of lack of sleep and not having a place to shower the next morning.
From Pamukkale we would continue by train to Selcuk so we could visit Ephesus early the next morning.

Whether your timetable is feasible depends on when you arrive in Pamukkale, how much time you intend to spend visiting Hieropolis, and the train schedule to get to Selçuk presumably on the same day if you intend to visit Ephesus early the next morning.

Overnight buses:
Nevşehir Seyahat - http://www.nevsehirlilerseyahat.com.tr/
Süha Turizm - http://www.suhaturizm.com.tr/
Metro - http://www.metroturizm.com.tr/en-default.html

Train timetable - http://www.tcdd.gov.tr/Upload/Files/...bassokeayd.pdf

Thank you!

Croesus - You attached a train timetable. How would you suggest we use the train to get from Goreme to Pamukkale?

You said "From Pamukkale we would continue by train to Selcuk"