Buses run by Lignes d'Azur (www.lignesdazur.com) link Nice with several of the valleys year-round – including Vallée de la Vésubie, Vallée de la Tinée and Vallée du Haut-Var.
The most direct route into Haute-Provence from the west is along the D202 from Digne-les-Bains, which skirts along the southern edge of several of the main valleys via gateway towns such as Barrême, St-André-des-Alpes, Annot and Entrevaux (it's essentially the same route followed by the Train des Pignes).
From the south, the D2204 provides a direct from Nice to both the Vallée de la Vésubie and the Vallée de la Roya. Depending on traffic, you can be right up in the heart of the mountains in just a couple of hours.
The Train des Pignes travels up into the mountains from Nice, stopping at Entrevaux, Annot and Digne-les-Bains, from where there are onward buses to many local towns and villages.