Aloha. Please keep in mind that at least 24 hours is standard for any sort of answer; I would even add some time to that, considering that this is the holiday season.
The route the girls are planning on taking is a well-traveled one along the Interamericana highway; with that said, this forum is less about budget traveling, and more about moving and living in Panama. I would recommend the Lonely Planet website, which has huge sections about travel through Latin America on buses and other cheap commercial transport.
As for my own experiences driving across Panama, I thought it was safe, well-maintained, well-marked and easy-to-use. There are easy to find bus stations in any town of any size, and if the girls speak Spanish, then it shouldn't be too much of a problem. You mentioned that girls have good judgement; that should keep them out of the bars and clubs in Panama City--let's hope.
Should you choose to try and find a chauffeur, this man might be able to help you:
Rene Guardiola Rene is a lovely man who runs a top-notch operation, has several bilingual drivers and could help you find the info that you seek.
Good luck!