Rhodos Buses can be slightly unpredictable,
so always best to arrive early for the bus.
To find out an up to date timetable please go to:
www.ktelrodou.gr/en/
Here is the link for Pefkos timetable as the above will show for the whole island:
https://www.ktelrodou.gr/en/dromologia/peukoi.html
There is also a FREE waterpark bus to Falaraki which is at 9:30am and can be full once it arrives to Pefkos (normal pick up is located by Pals Bar).
At any other times, there is no direct bus to the waterpark and would mean you will need to maybe get two different buses or a taxi once in Falaraki.
You might want to look at booking transfers within one of the local booking offices in resort to secure a seat and to be able to get there and back. Same with Rhodes town, the booking offices do trips to Rhodes town such as Rhodes by day or Rhodes by night.
You will find buses to go to Rhodes Town will have Rhodes Town written on the front or Lindos (which maybe will require a change of bus)
Main bus stop is from Pals bar/PBN but there is bus stops near Mingos supermarket up to Finas hotel and also by Pefkos Blue/Ziakis on the main road heading towards Lindos.
It could take between 1 - 2 hours depending on stops and direction the bus might take
(it could stop through many villages on the way up the island and you might have to change at Lindos and jump on another bus)
When heading home, you will board a bus that will say either Gennadi or Kiotari and possibly Lindos (with changing at Lindos)
At Lindos and Rhodes town there is a kiosk with someone you can speak too if your needing advice or directions.