Emperor Constantine VII was pretty clear that Bosnia was a part of Serbia in his time. That's the first mention of Bosnia in history. Other Byzantine historians of the era agree: John Kinnamos says that the Drina separates Bosnia from the rest of Serbia. Even a Roman Catholic source, Guesta Sclavorum agrees with Kinnamos on this. Even after Serbia fell under Bulgarian rule (~917) and reappeared some 10 years later, Bosnia was its part (927). The skirmishes between Hungarian and Serbian nobles happened exactly in what's today Bosnian Posavina.

Croatian king might've attempted to conquer Bosnia after the death of Serbian Grand Župan Časlav, however Bosnia was soon conquered by Emperor Samuel of Bulgaria and then Emperor Basil II of Byzantium. There are mentions of Bosnian governors helping quell the rebellion of Serbian governor Vojislav.

As Serbian governors became rulers of independent Doclea (Serb. Дукља/Duklja), Bosnia came under their suzerainty. Doclean rulers did appoint Bosnian rulers, who bore the title of knez at the time. At 1101 King Constantine Balduin (Serb. Контантин Бодин/Konstantine Bodin) died, and his realm was falling apart. In 1102 Croatia was subdued by Hungarian kings. Bosnia came under Hungarian suzerainty somewhere before 1139.

The Bosnian rulers did wear the title of ban, but that has nothing to do with supposed Croatian origins. It has to do with the Hungarian suzerainty of both territories. There are numerous speculations on its origins, but none has a valid explanation on the basis of Slavic origins. The first man who wore the title of ban (of Bosnia) was called Borić and appeared in the 12th century, as a Hungarian vassal, in ~1154. Before 1166, Bosnia became a part of the Byzantine Empire once again.

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Serbia (with Bosnia) was most probably under Roman jurisdiction initially. There is a letter from 878, which calls the then Serbian Grand Župan to return to his previous denomination. Roman Catholic sources from the 12th century call Bosnia: regnum Servilliae, quod est Bosna (Serbian Kingdom which is Bosnia). Even though here its separated from the rest of Serbia, it's clear that the two units were once under a single episcopate.

There isn't anything known about the religious life in Bosnia prior to the 12th century. The archbishops of Ragusa (Dubrovnik) were supposedly in jurisdiction of Serbian Kingdom, which is Bosnia. However, the monks seem to have followed the Byzantine rite (which doesn't necessarily mean that they were Eastern Orthodox, but it was seen as problematic in Rome nonetheless). In 1203 Ban Kulin and his people (whoever they were) were forced to give up on their beliefs on the Bilino Polje. However, even though the legate calls them Patareni, his own letter shows that they were not forced to give up on their dogmatic beliefs, just to recognize the primacy of the Roman prelate and to give up on schism. There is no mention of the Church of Bosnia, just of certain Christians.

It seems that early Bosnian rulers have followed the Roman Catholic faith, at least on paper. Ban Borić has given a property of his in Slavonia (which was Hungarian, but mind you, he was also a Hungarian baron at the time) to the Templars, while Ban Kulin erected a church near present-day Zenica.

At the turn of the 12th century into the 13th, a new dualist heresy came to Bosnia. While there are mentions of the Bogomils in neighboring Serbia and Dalmatia, the heresy in Bosnia doesn't seem to be orthodox Bogomilism.

A report to the Rome in 1232 might be the first time we hear of the Church of Bosnia. I will not dwelve further, but I will mention that the Church of Bosnia remained until the Ottoman times (perhaps further on), while the Bosnian rulers became reliable Roman Catholics and enforced the Roman Catholic faith ever since they became the kings in 1377/8.

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We have two mentions of the Serb identity in Bosnia during the medieval times from the bans themselves. Ban Matthew Ninoslav calls his subjects Serbs in a deal with Ragusa, while Ban Stephen II calls his language Serbian when giving the peninsula of Stonski Rat (Pelješac) to Ragusa. The 14th century shows increased influences from Serbia, as a specific type of the Cyrillic alphabet was imported by scribes from Serbia (sometimes erroneously called bosančica); Ban Tvrtko I was crowned as the King of the Serbs (=King of Serbia in this case), and even the crown might have been taken from the old Serbian dynasty.

However that soon changed. The title of King of the Serbs was soon replaced with the title of King of Bosnia just as King Stephen Tvrtko I (=Ban Tvrtko I) died (1391). The crown became the transpersonal symbol of the state, just like in the neighboring Hungary. As I've said, the Roman Catholic faith became the official one: Franciscans came during King Stephen Tvrtko I's time, and they were even allowed to beat Bosnian subjects into Roman Catholicism (under King Tvrtko II). New churches and especially Franciscan monasteries were being built and the Roman Catholicism became especially strong in the towns (the towns were being developed since 14th century only). King Tvrtko II was even given a title of the captain of the Christianity in expectation to lead a crusade.

Not only that, Bosnia was being increasingly westernized during the 15th century. Its knights partook in tournaments, the ruling clan (erroneously called dynasty) constructed for itself a German origin and a de-facto surname of Kotromanić. Western architecture started penetrating Bosnia, with the castle of Hrvoje Vukčić in Jajce being modeled after an Italian castle. That was a quite different process than the one in neighboring Serbia, and the differences deepened.

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When Bosnia came under the Ottoman rule, many things have changed. The Bosnian Church got shut down quickly, a part of the population certainly moved to Hungarian lands of Slavonia, while the population from Serbia settled in a significant amount. When he was passing through Bosnia in 1537, a Slovene called Benedikt Kuripešič hinted that the Catholic population of Bosnia were the original Bosnians. The Roman Catholic population of Bosnia, which was significant - especially in towns - was quite influential and seems to have retained the Bosnian identity. However, in the Great Turkish War (1683-1699) the population got decimated: they settled in great numbers in neighboring Slavonia and Croatia, as well as Dalmatia. The Bosnian Franciscan Province - once the mightiest Roman Catholic organization in the Balkans - became a shadow of itself; but the bishoprics in Croatia and Slavonia - some of them being shut down due to lack of the Roman Catholic population - got revived. With further political development, the population gradually adopted Croatian identity.

However, the Muslim population had its own Bosnian identity as well, and the idenitity was maintained. The upper classes of this society had a unique position in the Ottoman Empire, having the institution of the ocakluk timarlari, meaning that - unlike other upper classes of the Ottoman Empire - they inherited properties given to them from father to son. That formed a compact elite, which was closed to the foreigners. A great pride was taken of the fact that Bosnian provincial army played a great part in the conquest of Hungary and subsequent wars: due to that, they were given huge estates in Hungary and various other privileges. Also, a note should be taken that the process of conversion was much faster in Bosnia than in other provinces (a phenomenon that requires further research): that means that the population had longer time to build a collective identity than the Muslim population of other provinces, which was often subject to immigration and emigration, with no permanent upper class.

That being said, the identity was fortified due to traumatic experiences of the 19th century, where many Muslims were massacred, forced to emigrate from newly born Balkanic states etc.

One can find some examples where the Muslims identified themselves with Croats or Serbs, but the fact is that those examples are marginal and cannot be found in quantities too large. After all, it's not language or wearing same shirts what constitutes an ethnic nation: it's the common identification and common memories - just look at Switzerland.