score:5
Wikipedia's Ashoka article includes this map:
Its western border is the Seleucid empire which appears to be where modern-day Iran is (note that Iran I think might be ethnically Persian rather than Arabian).
It also includes modern-day countries like Pakistan and Afghanistan (which are Islamic but not exactly Arabic).
This map is labelled "Buddhist proselytism at the time of king Ashoka (260β218 BCE)":
It shows Buddhist proselytism reaching (beyond the Maurya empire) to Alexandria (which is in modern-day Egypt), and Antioch (modern Turkey).
This may not be "expansion of Buddhism" though, it's more like "envoys from the Buddhist empire".