This is impossible to know for sure, you'll just have to speculate. Ottoman records only show, for Bosnia, how many Muslim and Christian households were in a given area. Inter-faith marriages happened and were not uncommon. Even still, Ottoman/Turkish culture left a larger footprint in the Balkans than any modern nationalist will ever care to admit.

Maybe someone else can give a better answer, but that's the jist of it.

Permanent last names didnt take hold up until 18th century, early 19th in Bosnia. People used patronims like is common in Scandinavian countries. For example if your name is Ivan and your fathers name is Petar, you would be Petrovic, but your son would be Ivanic. The difference was if you were a noble, or one of your ancestors was well known for something (IE names like Alihadzic - went on a pilgrimage, Alihodzic - became a priest, or Alispahic - become a noble.)

There are several reason for your name: It is possible one of your ancestors had Turkish or muslim origins, and later converted to Christianity. There were several cases of it happening during conflicts in the Balkans, and sometimes peacefully.

It is also possible that your last name is just translation of the original name. That would especially be true if your family were brought as serfs to toil the land from abroad, which was a common practice up until Austrian ocupation. Dursun means halt/stop, the closest equivalent would be Stojic or Stanic. It is possible that the landlord that brought you was a Turk and instead of speaking your language he simply translated your names into something he could use. That was also common.

When you say a Turkish last name, do you mean it's a word in Turkish, or it's a last name that Turkish people have, or it's a last name that Bosnian people have that has a Turkish word in it?