I’m just posting this as I found it really hard to get information online and we made a few mistakes on the journey (such as leaving Palenque ridiculously early), so hopefully it will be useful for others.
For various reasons, we wanted to travel from Palenque to Bacalar during the day but the ADO bus company only offers night buses. If you want to travel during the day, you need to take a colectivo to Zapata. These leave from the colectivo terminal (Allende and 20 de Noviembre) hourly from 5.30 a.m. and cost 40 pesos. The journey takes about an hour so I would suggest getting the 8.30 a.m. one. From Zapata there is a bus to Chetumal at 10.30 a.m. It costs 322 pesos and leaves from the same terminal you get dropped off at. The bus company is TRT and the tickets are sold at the ADO counter but not by ADO staff (slight confusing).
We got off the bus near Chetumal at a town called Huay Pix. Once off the bus, we crossed the road and flagged down a colectivo which runs between Chetumal and Bacalar. This cost 25 pesos and took about 20 mins. We arrived in Bacalar at about 6.30 p.m.