We want to spend an overnight in Mostar but it looks like the tours won’t let us leave the group to spend the night. We were then thinking about just taking a bus, but we’ve heard crossing the border can be a frustrating experience adding hours on to the travel time. We are planning on going next May. Any advice is most welcome!
You could rent a car and stop at the waterfalls. You wouldn't need the car until you're ready to leave Dubrovnik.
You could rent a car and stop at the water falls and at Blagaj Tekija (one on the way up, the other on the way back). But as a general rule I dont drive on holiday. Actually I no longer own a car. On holiday I would rather be looking out the window and not stressing over the road and parking and wasting the time it takes to pick up and return a rental. And honestly I am a bad driver and worse with luck and dont want to become part of 2476 traffic fine / theft / accident related threads on the forum.
On the other similar thread I mention that I have been to Bosnia and Croatia three times each and have yet to see Mostar, so I am fixing that in a few weeks and spending a night in Mostar before returning to Sarajevo. But I hired a driver. The guy goes to Dubrovnik too.
We took the bus. Was no big deal.
We did a similar trip in May- we flew into Dubrovnik, spent the night, and travelled to Mostar the next day to start our trip around Bosnia. We used Taxi Pajo to drive us from Cavtat to Mostar and they were great. It was 160 EUR for one way. We also used them for a trip from Mostar to Blagaj which I highly recommend if you have the time (beautiful monastery on a river). In terms of crossing the border, it was extremely quick- basically just a short pause exiting Croatia and another short pause entering Bosnia while they checked our passports. There weren't any other cars going through at the time.
This is the info for Taxi Pajo: https://taxipajo.com/en/home/
Bus, excellent idea. Where can the OP find the bus schedule to Mostar, by way of the falls on the way up and Blagaj Tekija on the way back? That would be great.