Driving in Bosnia is very easy, and if you rent a car and drive, you be able to stop and see things. The drive from Mostar to Sarajevo is very beautiful in parts, along the river. There really aren't many (any?) official "viewpoint stops" to pull over off the road on this drive, but I still stopped numerous times to take pictures. The bus would take the same route - and so would the train (between Mostar and Sarajevo). My only regret about driving was that I did not get to take the train ride, and I love trains.
Obviously one downside of driving is the extra expense to rent a car and then just park it for a few days in Sarajevo. You can probably find a hotel with free parking, though - mine did. I didn't move my car either for a few days in Sarajevo once I arrived there, but I didn't go back to Dubrovnik - I drove on through Bosnia and back to Zagreb, eventually, stopping for a few nights at towns along the way. There is more to Bosnia than just Sarajevo and Mostar.