In all the resorts you will find a bus timetable at the main bus stop. You can also find English language, local newspapers, such as the 'Corfiot', which has a section detailing bus timetables.
Yes, the local bus service is very reliable, however, you should be at bus stops at least 10 minutes before departure time, if a bus arrives early it will rarely wait.
In the resorts, look out for the taxi stop and you may find there will be a printed list of taxi numbers. Local taxis generally serve the local area but if you need to go further you should be able to book the taxi directly with the driver. In Corfu Town there are two main taxi stops. One is at the Liston and the other at San Rocco square.
You should note that on changeover days, especially Mondays and Fridays it can be difficult to find taxis as many get booked for airport transfers. If you take a taxi to another resort for the evening, you should always book your return journey with the driver.
You should arrange a price with the taxi driver before you set off. Prices may vary according to resorts and distances.