Cavaillon has regular bus services to many Provençal towns, mostly provided by LER.
Avignon (€2.70, Line 22, 45 minutes, four daily Monday to Saturday, two on Sunday) Stops in Cavaillon en route from Avignon’s TGV station (a couple of buses also run from Avignon's central train station), then travels on to Bonnieux, Apt and Forcalquier.
Cavaillon's train station is handy if you're accessing the Luberon by train. There are regular links to both Avignon's central station and the TGV station (€8.10, 40 minutes, every two hours).
From here you can catch a bus into the Luberon Valley – although it might just be easier to catch the Avignon bus straight from the station in the first place.