This is not a timeline, but rather a nebulous idea.
What would have been necessary for Buddhism to become an established and strong religion in at least part of Southwest Asia up to the equivalent of our times? I feel as though perhaps the best way for this to occur would have been if Alexander the Great had successfully conquered a larger span of India and had lived longer. The Indian monarch, Ashoka Maurya, rises against the Alexandrian forces and manages to drive them back a considerable distance, perhaps the Indus River, eventually cementing a powerful kingdom throughout India as in OTL, but bordering a far greater (though rather spread-out) Alexandrian Empire. The idea currently rattling in my mind is that if Ashoka were to convert at about the same time as he did in OTL (about 262 BC), Alexander the Great would by then have been growing older, with some of his youthful intensity and vigor cooling down. When Alexander musters his forces to attempt a reconquest of the lost Indian territory, Ashoka, having converted to a nonviolent religion, decides to meet with the Macedonian personally. Alexander has something of a dichotomy in his character between the stubborn, impulsive, alcohol-quaffing "berserker", and the Aristotelian, calculating, erudite "philosopher-king." Ashoka's character, I feel, would have appealed to the latter side of Alexander. As Alexander grew old, I feel that he would have always had a sense that he was alone in the world in a certain respect, due to the vast degree by which his achievements and abilities outstripped those of the people around him. To meet a contemplative man who, like him, had also achieved great military and political power would have been an important experience to an older Alexander. Ashoka, for his part, would have been a freshly converted man, and that always involves zeal.
Would Alexander have converted? I cannot be sure, of course, but let me assume that he did (if anyone thinks this too unlikely, please correct me). I envision a spread of Buddhist missionaries through Iran, and formal debates between the Zoroastrian priesthood and bhikkhus from the Buddhist sangha. I feel that Zoroastrianism would have already been weakened by Alexander's destruction of the royal library in Persepolis. I can't find much information about Zoroastrianism under the Seleucids, but I feel that it would have been weakened also by the fact that it described the world in fiercely dualistic terms of good against evil, and yet as far as heathen conquerors go, I don't believe that the Greeks were as heavy-handed as even the Romans would be. That kind of undercuts the dualistic logic, seeing as the Greeks had overthrown a strongly faithful Zoroastrian monarchy. With the introduction of Buddhism to Iran, a religion would be presented that appealed to everybody: the Greeks because it is a highly ordered and philosophical way of life that would likely remind them strongly of Socrates and his disciples; the Iranians because it was a religion that explained life not in dualistic mythology but according to the laws of nature and of kamma-vipaka. The thing that really counts is whether or not Buddhist monks became directly involved with ordinary people, teaching them and receiving alms-food from them.
I don't think I'll pursue this further unless I get some outside feedback, however. :B