We are going to be traveling in Croatia in June and would like to spend two nights in Mostar between Korcula and Dubrovnik. Going from Mostar to Dubrovnik does not seem to be a problem. Is there a bus connection (or connections) to get from Korcula to Mostar?
Although I understand your interest, this is a slow detour with time-consuming immigration formalities between countries that are testy with each other. Certainly Mostar needs your money, but unless it's family-related, why two nights? You might find transportation and (Russian-financed ... ) tourism already more developed in the UNESCO WHS of Kotor, Montenegro. (I'm contrasting that as a gorgeous medieval town with nearby resorts, that didn't suffer wartime damage.) Just an idea to consider.
We hired Ermin Elezovic to transport us from Mostar to the Korcula ferry. He played tour guide on the way, we stopped at Pocitelj, Ston, and at a couple of Peljesac wineries en route. It was delightful and I would recommend it.
We did the same thing in 2012. There was a bus that left Korcula in the morning around 9:00. We arrived Mostar by early afternoon. The border crossing was a little slow, but no problem. Mostar is definitely worth a visit. It's just a beautiful town, although the very visible scars from the war remind you of its recent trauma. We stayed at Pansion Cardak which I highly recommend. There's a nice shared kitchen, and the owners were very helpful. They even drove us to/from the bus station. I would also recommend Pocitelj as an interesting day trip. Our hostess hooked us up with a taxi who drove us there, waited, and brought us back for 25 euros.