well, it certainly ought to be doable. Basically every language used by Moslems from Morocco to Pakistan from southern Africa to the central Asian steppes used some variant of the Arabic alphabet, and as you pointed out, the Bosnians did too. 1941 as a date for outlawing the script is awfully late OTL, if it survived that long we might even be able got get away with a POD after 1900.How could the dominant language of Bosnia become Bosnian written in Arabic script?
Preferably without Bosnia still being part of a Muslim empire ruled by non-Slavs...
well, it certainly ought to be doable. Basically every language used by Moslems from Morocco to Pakistan from southern Africa to the central Asian steppes used some variant of the Arabic alphabet, and as you pointed out, the Bosnians did too. 1941 as a date for outlawing the script is awfully late OTL, if it survived that long we might even be able got get away with a POD after 1900.
At a guess, the biggest problems might be 1) the dominent Christian elite (whether Serbian Orthodox or Austrian Catholic) 2) the nationalist expansionist proto-empires.
1) the Serbs didn't dare be too too horribly oppressive to the RC Croats, as if things got TOO bad, they could call in the Austrians. The muslim Bosnians have the protection of ... ?Albania? (since the Ottomans are whom everyone else in the Balkans were rebelling AGAINST). Similarly, I suppose that Serbian communities in RC lands could call on Serbia for help if too oppressed.
2) If a truly federative *Yugoslavia (rather than a re-branded Greater Serbia), possibly including parts of, say, Bulgaria, formed, then there might be greater respect for various minorities, and the Bosnians might keep their own script.
OTOH, Cyrillic and Latin letters are closely related (both being ultimately descended from Greek), and it's really not that hard to learn the one knowing the other - so, e.g. reading signs on a trip isn't that hard. A semi-Arabic alphabet would be a lot harder, so might make it harder for commerce?
What dominant Christian elite?
Anyway, it's a simple POD. Just don't have Bosnia become communist, and preferably not part of a Yugoslav state. But even then, the Serbs and Croats had never used the Arabic-derived script.
A further back POD would be no Russo-Ottoman War in 1877, or the Ottomans win. Bosnia eventually becomes autonomous, and then independent. Without the war, there is no ethnic cleansing and mass exodus of Muslims, so Bosnia retains its Muslim majority (about 50% in 1876). There would be little incentive to abandon the script and the Muslims would be the numerically and culturally dominant sect.
Does this mean that the most likely prospect for Arabic-script Bosnian would be autonomy within the Ottoman empire rather than outright independence?In the event of Bosnia somehow gaining independence, it would be a brief existence, as it is surrounded by hungry neighbours, wherein the Arabic-script would be suborned by whichever power got them first.
I don't know- I think a less ideological regime than Yugoslavia would do it. Yugoslavia very much wanted to promote a single "Serbo-Croatian" language, and the Arebica was the least entrenched compared to the Croatian Latin alphabet or the Serbian Cyrillic. However, if someone like Austria who didn't have an interest in promoting Yugoslav nationalism (indeed, just the opposite) was in charge, they may promote the use of the differing alphabet as a way to decrease similarity between the very similar languages.