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 terminus at 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 ADO 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 towards Campeche, Chetumal/Cancun or west towards Villahermosa.
South towards Ocosingo, San Cristóbal de las Casas
From the ADO bus station, walk south approx. 500m along highway 199 to the junction with the road leading to the Palenque ruins. This is a good place to hitch south towards the waterfalls at Agua Azul and onwards to Ocosingo and San Cristóbal de las Casas. Alternatively, keep walking another 300m to almost the southern edge of town and you will find a Pemex gas station and a police post with 'topes' (speedbumps) so traffic has to slow right down.
Hitchhiking from town to El Panchan/Palenque ruins and vice versa
El Panchan is 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 :)
Tips and Tricks
In order to enter the arqueological site you have to pay, and by paying you get a wristband that from time to time you need to show in certain places (like some special jungle paths, but this is usually on the most touristic days/places). There is a way to enter without paying and that is to take a left right before the entrance (a stone arch with the people asking you to pay) and go to the restaurant and hut complex, if you keep walking thru the restaurant and try to keep your walking paralel to the main entry road to the arqueological complex, soon you should be able to walk thru the bush or find a path to it without paying. This can be simplified if you come right after the entry offices close as they leave the gates open (somewhere around 18hs but that might change depending on the season), which shows how much they care about the entrance fee. A justification to do so is that you can stay in the arqueological site for weeks if not months and they would expect you to pay the entrance every couple days, which is absurd if you are staying inside and already paying for lodging/camping. Nobody will hassle you about your lack of wristband, specially if you explain that you are staying at some camping place and that you take it out when you shower and forgot to put it back in (be creative or most people will have the same excuse). Entering the actual arqueological site (where the ruins are) is a bit more tricky (Hint: walk thru the river against the current until you reach the site). Id say its decent to consider paying once for entrance to both the arqueological site + jungle and the ruins itself, but you might feel like the whole place deserves a month long stay and then you might feel like finding your way around it without going bankrupt. Another thing to do is to hang out by the main road and when you see people on their obvious way out ask them if they can give you their wristbands/tickets.