I down think People fo Bosnia converted to Islam any more or less than people of other parts of europe, like Serbia or Greece or Hungary or Bulgaria. Its just that the Cristians never managed to get rid of the Muslims in Bosnia like they did in Serbia or Greece. Dont forget that large parts of all these balkan countries were muslim and they were all killed and expelled. Only in Bosnia and Albania did they put up a fight and manage to hold on despite the odds.Actually:
"Several factors appear to have been behind this process. Most important was that Christianity had relatively shallow roots in Bosnia prior to the Ottoman domination. Bosnia lacked a strong Christian church organization to command a strong following—the result of a scarcity of priests and competition among the Orthodox and Roman Catholic Churches and schismatic Bosnian Church, which collapsed shortly before the Ottomans arrived. This left most people religiously unengaged and receptive to the appeal of Islam’s institutions. This receptiveness was aided by the development among many people of a kind of folk Christianity centered on various practices and ceremonies that was adaptable to a form of folk Islam popular at the time of the invasion."
"One theory as to why conversion to Islam was more prevalent in Bosnia than other places in the Balkans is the possibility that the Bosnian Church practiced bogomilism. Bogomilism was regarded as a major dualistic heresy by the Catholic Church and against whom Pope John XXII even launched a Crusade in 1325. Thus many adherents of the Bosnian Church were more receptive to conversion to Islam. In fact, in the Bogomilian tradition, there were several practices that resembled Islam: they rejected the veneration of the Virgin Mary, repudiated the Cross as a religious symbol, they considered it as idolatry to bow down before religious images, relics or saints, and even prayed five times a day (reciting the Lord's Prayer.)"
One thing that helped Bosnia was being taken over by Austria who prevented the Serbs from expelling all the Muslims. The serbs simple didnt have the power and Austrians had no problems with the muslims in Bosnia as they were not a threat to them.
After the Austrians were kicked out of Bosnia, a Serbian king tried to get rid of all the Muslims, Zimbabwe style, by taking all their land. but thankfully this Serbian king was replaced by hitler, who just hated the serbs, and to a great degree got rid of them instead.
So muslims in Bosnia were probably saved in part by their own willingness to fight. by the mountainous terrain by the Austrian empire and by nazi Germany.
And of course by the communist dictator Tito, who made everyone forget ethnic hatreds for 45 years.
And after that they were saved by their heroic fight and by bill Clinton and USA.
It's always someone or some historical tectonic shift that saved them. And now they are not going anywhere.