The intercity buses are run by the Transport de les Illes Balear; these are regular, comfortable and cheap.
Search for TIB Mallorca on the web to find the current timetables (the bus service is usually punctual). Note that bus frequency drops to about 50% during weekends and holidays, so plan ahead. Most buses take at least two bicycles in their luggage compartment and start off from the main terminal under Plaza d'Espanya