The reason it exists is so bizarre too. It stems from the rivalry between the republics of Venice and Ragusea (modern day Dubrovnik). Venice was gradually asserting control over more and more of the Adriatic coastline and Ragusea didn't much fancy sharing a land border with its rival, so it just gave up one tiny stretch of land each to its north and south to the Ottoman Empire. Venice would therefore have to come by sea or risk angering the Ottomans. Eventually Austria manages to annex the Dalmatian territory of both Venice and Ragusea, but the Ottomans still held those two tiny strips of land. The Ottomans were not typically on the best of terms with Austria, and they held on to the two tiny bits of Adriatic coast up until the treaty of Berlin in 1879. By this point, Neum (the Bosnian one) had been part of Ottoman Bosnia for 179 years, so the borders were pretty damn entrenched, and they survived through the shifts to Austrian, Yugoslav, and eventually independent Bosnian-Herzegovinan political structures. So a petty but clever move of hiding behind a bigger empire in the 1600s created the tiny bit of Bosnian coastline today.

But it has to share it with Herzegovina, so more like 6 miles for Bosnia and 6 miles for Herzegovina

Neum is actually in Herzegovina but whatever. It's inside a bay that Croatia controls from both sides, and in fact has a bridge over. If B&H got naughty again, they could turn it into a lake just by dumping enough clay from the bridge.