This is a tricky question, and one might ask the obverse - why is it that Bulgaria, Romania, Serbia, and Greece have generally low Muslim populations as opposed to other Balkan countries that were under the Ottoman Empire (Montenegro, Macedonia, Bosnia and Herzegovina, Albania, Kosovo)?With Romania, it is most probably linked to the fact that the Danubian Principalities that would later form today's Romanian state (mostly the Old Kingdom - Wallachia and Moldavia) were never really directly incorporated into the Ottoman Empire, but were rather vassal states. They were run by mostly Greek-speaking merchant elites who held the titles of hospodars or something akin to princes. These were Stambolite Greeks also known as the Phanariotes, and were part of the upper class of Ottoman society. To this day, many Romanians' last names betray this period of Greek cultural hegemony in which Bucharest was a center of Hellenic learning.
With Greece, Serbia and Bulgaria, this is a trickier story. All these countries, while not having majority Muslim populations, did have sizeable Muslim towns. By the time nationalism emerged in the early nineteenth century as an ideology that supported the foundation of these nation states, the majority of the urban population in all three countries was Muslim. What happened to them?
Well, many of them were expelled, from Serbia largely in 1862 after riots in Belgrade and the bombardment of the city by the pasha, but already from 1830 onwards with the proclamation of Serbian autonomy. There are many reasons why Muslims were considered incompatible with modern nation states. Some of these had to do with ideas about the backwardness of Islam and the tenacity of Christianity, supported by Orientalist perceptions of the Great Powers. Muslims were not under the authority of the Serbian autonomous Principality, also because the Porte was cautious in releasing authority to the emergent Serbian nation state. Autonomy at the time meant originally judicial authority over Christians, and then later Jews and Gypsies. The Muslim population also preferred to maintain this status of dual authority due to notions of loyalty to the Sultan as well as financial benefits it would bring. Having a sizeable Muslim population was considered backwards, and incompatible with the modernizing project that would allow Serbs to join the European family of nations. This project was largely spearheaded by Habsburg-educated Serb cultural elites who worked towards political unity with other South Slavic nations. In this sense, the expulsion of Muslims took place through a gradual series of negotiations and contracts between Belgrade and Istanbul, particularly since 1867 when the idea of Muslims as an "occupying force" was cemented, particularly through the involvement and support of the Great Powers. The Muslim population of Belgrade, Smederevo, Soko, Fethislam (Kladovo) and Šabac was expelled and their property bought by the Serbian state, usually for pennies on the dollar.
After the Berlin Congress in 1878, Serbia was granted the Niš region, largely as appeasement for not having received Bosnia which went to Austria-Hungary. There was a sizeable Muslim population there as well, but it was largely expelled this time quite violently by the military-state apparatus which occupied the area. Many of them had fled previously because of the Russo-Turkish War, in which atrocities at both sides led to huge population movements in Bulgaria and the Niš region. The number of Muslims that were expelled or voluntarily fled the war is projected by some authors to be around 250 000 people, but it is tricky to determine and is a politically contested issue even today. Muslims did become citizens of the autonomous Bulgaria after 1878, and its independence in 1908, but many chose to relocate to Macedonia and Istanbul. There is still a Muslim population in Bulgaria (some 750,000 Turks and Pomaks mostly, so about one tenth of the population), and there have been period attempts to "Bulgarianize" the population, most famous being the quite recent campaigns during Todor Zhivkov in the 1980s, which led to further emigration, mostly to Istanbul.
The areas which were incorporated into Serbia after the Balkan Wars of 1912, and the establishment of similar "civil" ideas of citizenship, namely Kosovo and the Sandžak region (which is still part of Serbia today) maintained a majority Muslim population. There were some attempts at resettlement into Turkey in the 1920s that may have numbered upwards into the 200,000 people number, but most of the emigration, particularly from Sandžak, has been economic.
In Greece, the majority of the Muslim population was also expelled during the wars of national expansion, but a sizeable Muslim population remained until the Population Exchange of 1923. As I mentioned, the idea that nation and religion were one was generally a component of early Balkan nationalism, and the Greek, Serbian and Bulgarian states all wound up to be based on this idea. After the First World War (which stretched really from 1912 to 1922 for Greece and Turkey), some 2 million people were moved - about 1.5 million mostly Turkish-speaking Greek Orthodox peoples of Anatolia were sent to Greece and some half-million mostly Greek-speaking Muslim peoples of Greece were sent to Turkey. The ethnic homogenization of these states was considered to be stabilizing and good for the further development of the nations, but had profound detrimental cultural and economic effects that are felt to this day in both areas.
Later Balkan nationalisms, namely Albanian and Bosniak nationalism (but also the Macedonian Liberation struggle) were all based around the concept of language or region, rather than religion, and were highly religiously inclusive. In Bosnia, this clashed with pre-existing Serb and Croat national movements, and although the Austro-Hungarians particularly supported an inclusive version of bošnjaštvo (Bosnianness), this was largely not accepted by the intellectual elites of Orthodox and Catholic cultural movements who preferred to see themselves linked to the neighboring "modernized" nations of Serbia and Croatia. In Albania, the movement was largely successful at bridging the religious gap, but this was a tenuous process (Albania was also only created in 1912), and even in the early 1900s, many Albanians saw themselves as loyal to Istanbul rather than the Albanian national cause - there was a significant Albanian contingent in the Young Turks until quite late.
TL;DR: There used to be Muslims in all Balkan states, although in varying proportions. Early Balkan national movements that were ethnically and religiously homogenous gained recognition first from the Great Powers, starting with Greece and ending with Bulgaria. Albanian and Bosnian nationalisms emerged quite late and were able to incorporate varied religious groups into their respective concepts of state administration.
I can provide sources for all this if anyone's interested further, I just didn't really have the time now and dinner is on the stove. It is important to note that Bosnia has a sizeable Muslim population, but is not a majority-Muslim state. The same goes for Macedonia. Albania has a large Orthodox Christian population, and Kosovo used to have one as well until relatively recently.
