We see, in Syria, recently, Chechnya, a little ways back, and Afghanistan decades ago, fighters flock to the cause. Why, when Muslims were under direct threat, in Bosnia, did they not assist? Especially, since the Serbs were Christian?
The short answer is that they did.
In fact, the Bosnian government actually organized a detachment of foreign volunteers, called Mujahedin in the ICTY reports. They were largely made up of North Africans and men from the Middle East, however they did recruit from the local population as well. The groups of locally recruited Mujahid and foreign fighters aren't distinguished seperately by the ICTY, largely because they couldn't be.
That being said, the main difference between Bosnia the other war-zones that you mentioned was that the Mujahid were unpopular with most Bosnians due to the fact that they didn't need of more soldiers, especially those espousing a far more extreme version of Islam than much of the local population did. What was needed at the time were arms, in part due to the UN arms embargo, which Saudi Arabia, Turkey, and Iran offered to provide in spite of the embargo. Iran sent the largest amount, also having reportedly sent some Hezbollah fighters.
As for their role and cooperation with the Bosnian Army proper:
In the first Tribunal judgement to deal with the presence of foreign Muslim or Mujahedin combatants in central Bosnia and Herzegovina, the Trial Chamber found that Enver Hadzihasanovic exercised effective control over a detachment of such forces. It found that Mujahedin members severely beat and psychologically abused five civilians from the Croatian and Serbian community in Travnik and murdered Dragan Popovic in October 1993 in the Orasac camp. The Trial Chamber found Enver Hadzihasanovic guilty of failing to prevent these crimes.
Main source is ICTY documentation as well as summaries and press releases regarding said documentation.
As part of the Army of Bosnia fought many of the Mujahideen of the Islamic countries. In June 1992, their number reached 3,000. Bosnians received support from various Muslim groups. According to the reports of some US non-governmental organizations, several hundred fighters of the Islamic Revolution Guards fought in the ranks Bosnian forces during the war. They were mostly from Afghanistan, Albania, Chechnya, Egypt, Iran, Jordan, Lebanon, Pakistan. Saudi Arabia, Sudan, Turkey and Yemen. By the end of the war their number has greatly increased of the Mujahideen were created six "Muslim infantry brigades", several separate battalions. These units after the war were accused of committing numerous war crimes against Serbian and Croatian civilians and prisoners of war.
The core of volunteers who fought on the side of the Bosnians were Mujahideen. The number of Arab mujahideen who arrived to Bosnia in a roundabout way, and fought on the side of the Bosnians still not been established: the numbers fluctuate up to 6000 people.
Only from May 1994 to January 1995, Iran sent more than five tons of weapons and ammunition in Bosnia. The Shiites of the Lebanese movement "Hezbollah" also went to Bosnia by volunteers.