North towards Villahermosa, Campeche, Chetumal
From the ADO bus station, walk north approx. 2kms along highway 199 where you will find a bus stop and the first topes (speedbumps) on the road out of the city. Traffic has to slow and it is possible to hitchhike here. Unfortunately, there is a still too much local traffic here and it could be a long wait.
Alternatively, take a colectivo from highway 199 to the start of the northern suburb/barrio of Las Joyas (at the turnoff for highway 10). Walk about 500m north along highway 199 till you reach the outskirts of the city. (This spot is approx. 5.4kms walk from the bus station). The advantage of this place is that you will have cut out all the local traffic and should be able to at least get a ride to the main interstate highway 186 (20kms away) where it will be much easier to get a long distance ride either east or west.
Hitchhiking from town to El Panchan/Palenque ruins and vice versa
El Panchan is the where a lot of the hostels/ camping places are located a few kms from the ruins. There are a lot of possibilities to wildcamp around there too. It is easy to hitch the 6kms on the only road from there to Palenque, and vice versa.
From El Panchan, there is a park entry toll-point just past the turnoff for the road to the hostels/camping, so the traffic will be going slow at the turnoff where you will be standing to get a lift into town. Many tourists will be returning to town in hired cars from the ruins. Also, locals working at the ruins will pick you up more than the tourists.
From Palenque, walk south 500m from the bus station to the start of the road leading to the ruins. There is a lot of space for vehicles to pull over.
If you are out of luck and forced to take a colectivo, haggle like crazy. The price is a total rip-off relative to the distance travelled, and if you haggle with a smile, most times they will relent :)