Were the Bosnians just the Serbians who converted to Islam because of the Jizya and Turkish policies?
Your question is begging the answer that Serbians predated Bosnians/Croats, which is incorrect. All three are linked to proto-Slavic groups, yes, but came to inhabit the Balkan region separately. Bosnian ancestry literally in Bosnia, with a secondary wave of Serbs and Croats in other areas of what came to be known as Yugoslavia.
The idea that Bosnians were Serbs who converted to Islam is a direct result of the religious propaganda used to justify the conflict in the 90's, implying that Serbians always had a divine right to the land that Bosnians/Bosniaks inhabited. Which is incorrect.
The complication arises from the fact that Bosnia, Kingdom of Bosnia, etc., was occasionally incorporated into Serbia and Croatia, respectively, but ultimately always ended up regaining its independence.