In this paper we present Bidirectional Multicast RPL Forwarding (BMRF), a new multicast protocol that combines the best features of the Routing Protocol for Low Power and Lossy Networks (RPL) multicast on the one hand and of Stateless Multicast RPL Forwarding (SMRF) on the other hand. The main features are bidirectionality and the ability to offer a choice between Link Layer broadcast and Link Layer unicast for which the threshold to decide for a mote, which link layer mode to choose, is mainly based on its number of interested children and the duty cycling rate. An implementation of BMRF is realized in Contiki. Our measurements show that BMRF, when using the optimal configuration, results in less radio transmissions, and less energy consumption, and higher packet delivery ratio compared to SMRF, often at the cost of a higher end-to-end delay.