It seems to vary. I walked quite a bit with two people from Quebec, and occasionally the woman needed to take transport because of knee problems. Quite often there was a local bus available that traveled between smaller towns/villages. (These usually didn't run on Sundays though.) At other times she needed to take a taxi.
I think you will find lots of busses between towns on the Camino Frances. Check with the tourist agency in one of the larger towns...they can give you maps and tell you how to navigate busses through the smaller towns. Buen Camino!
For those pilgrims requiring buses between towns, the http://www.alsa.es web pages contain bus routes and timetables and prices. It is possible to go from Burgos almost all the way to Santiago d.c. by bus. For example, Buses connect Burgos, Fromista, Sahagun (via Palencia) Leon, Astorga, Ponferrada. Furthermore, there is a bus which leaves Portomoran around 9.00 am which will take you to Santiago d.c. via Palas del Rei. Buen camino Jrs
For timetables of buses I would also suggest you go to the local bus station (times are posted at the offices). Or ask the albergue, most locals seemly have a timetable in their heads as nothing is posted at bus stops.
Also if you wish to pre-plan before you leave home you should look for the local council’s website. The example given above for Portomarin is one. The website gives far more details of bus times and routes than ASLA as the service is run by a local company.
due to knee problems I had to take a few buses when I did my camino in September last year. Either ask at the albergue and they will show you where the bus stop is, or ask at the tourist office in the bigger places. I found the albergue operators always knew when the bus left and where from, cheers, Jane