Greece has a national bus service called KTEL. This runs on Crete as well and it is cheap, safe and reasonably punctual.
KTEL in West and Central Crete has its own
web site where you can download current time-tables..
The phone numbers are 2831022212 for Rethymnon, 2810 221765 for Heraklion and 2821093052 for Chania. Don't assume that they will speak English well or at all. They will also reply to emails enquiries and will do so in English.
There will be far fewer buses to tourist destinations shown in winter than there are in the summer months. It is not possible to check summer time-tables at other times so you'll need to go back to the site closer to the time at which you want to travel.
As a rule, there are a number of buses per day between the main cities and at least two a day to even the smallest villages, if only to take children to and from school.
The buses between Heraklion and Rethymnon - Chania run hourly from 5.30 am
(first departure from Chania and Heraklion) to 8.30 pm (last departure from
Chania and Heraklion) and possibly later in the summer months. This can pose a problem for night arrivals at the airports.
The journey between Chania and Heraklion takes a little over two and a half hours - do enquire though, there are some express buses as well as a few that are particularly slow.
The buses are in good mechanical condition. They are not as old as the one in the picture but not necessarily very recent models! Most buses have air-conditioning. The drivers are safe and competent and accidents are extremely rare. It is far safer to take the bus than drive a car.