Sorry to say that cost or safety don't enter into the equation. You are NOT allowed to take a rental car from one country to the other. Can't be done.
So . . . for busses (they are safe) you can check these sites for schedule and fare information. Cost will depend on whether you use a series of "local" buses or the "express" busses that run between the countries. The express busses are nice, quick (relatively speaking), noisy (bring earplugs) and COLD (bring a blanket or coat).
Enjoy your trip.
As StxSteve says, you can't take a rental car from Panama to CR. However this may be of interest if you wanted to drive in both countries. Vamos rental can arrange a car in Costa Rica which you drop at the border, then pick up another car at the Panama side. Not sure how that would work in reverse but you could ask them?
So by bus it roughly takes 16 hours one way?
!6 hours - maybe from PC to San Jose - but not from PC to the CR border - I guess it depends on where you are going in each country.
It is about 400 kilometers from PC to David - maybe another 60 to the border with CR to Frontera - which is little bit like an outlet mall - nothing like the states though - just lots of small shops selling mainly to Ticos coming across to shop in Panama. Dusty, dirty little town but kind of interesting due to being a border crossing.
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