Buddhism, like Christianity and Islam, is a missionary religion. Between 500 BC and 500 AD it spread relatively easy from North India to the rest of India, South East Asia, Indonesia, China and Japan. One major feature of a missionary religion is that it is pretty sure of itself and therefore quite inmune to other religions, therefore quite inmune to change.
Once crossed the Middle East and the whole of North Africa it hypothetically could have rooted in the Manding or Mali Empire (roughly from 1200 to 1600), because their kings, although converted to Islam, didn´t force their subject to the same religion.
