I chose to travel both ways by train because it's more confortable than the bus. I saw the bus but it didn't appeal to me at all. If you plan a day trip you may as well buy a return ticket in Kaliningrad. Or else if you buy your ticket in Zelenogradsk you need to tell them which station in Kaliningrad you want to travel to like Yushni (South which is the main one) or Severni (north which is in the center) as there is a price difference.
There are several buses going from Klaipeda, via Nida, to Zelenogradsk and Kaliningrad.
We paid 11 Litas per person from Nida to Zelenogradsk in April 2006, and a local bus from Kaliningrad cost us 24 rubles per person.