How did the Graeco-Bactrian empire come to accept Buddhism?

Question

I am trying to find something along the lines of acceptance of Buddhism by Graeco-Bactrians. I would like to learn more about western India and Graeco-Bactrian empire especially from a political, cultural, ethnic and religious point of view and interaction between Indians, Greeks and eastern Persian tribes but i do not know which source to refer for this information.Can people here please provide me a road map for learning history of this place.

Edit: I would like to learn more about time frame between Alexander and Mahmud Ghazni especially the area of Gandhara. My goal is to understand how the society (especially ethnic and religious makeup) shifted over the course of this period.

Answer 1

The question, as is, covers a long period between Alexander (d. 323 BCE) and Mahmud of Ghazni (b. 975 CE) and the ethnic and religious influence changed extensively over the period of more than a 1000 years.

So, I will focus on Gandhara during the early stages, immediately post-Alexander, and with particular emphasis on Buddhism (Gandhara was in the question title before subsequent modification).

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Ashoka of Mauryan Emprire

Ashoka (son of Bindusara) would be the start of Buddhism in Gandhara. He was a significant emperor of the Mauryan Empire (322 BCE - 185 BCE). This period is much earlier than the Ghaznavid Empire (975 CE - 1187 CE).

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Buddhism under Ashoka

The significance of Ashoka and Mauryan Empire to Gandhara, in terms of acceptance of Buddhism is on several levels:

1. The Mauryan Empire was the first empire immediately after Alexander to adopt Buddhism as one of it's religion, i.e. early stages of Graeco-Buddhism. To be clear, Buddhism was the dominant religion of the Kushan Empire and the basic repertoire of Buddhist iconography (art style) was developed during the Kushan period around the first century CE, but this was much later than the Mauryan period.
2. Ashoka started his career in Gandhara as a governor before he became the Emperor (see Wikipedia entry on Ashoka)
3. Ashoka was the first Mauryan Emperor to convert to Buddhism, after he became the Emperor
4. He actively promoted Buddhism throughout the empire (and beyond) with his edicts on Buddhism.
5. As an indication of the close ties to Gandhara, Ashoka's son, Kunala, was also the governor before he became the next Emperor.

Ashoka succeeded Bindusara as emperor in 270 BCE, while his son, Kunala, became the governor of Gandhara ...

source: The Grandeur of Gandhara (Algora Publishing, 2011)

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Ashoka's Legacy

Ashoka's legacy is the spread of Buddhism, to Gandhara and the rest of the world - source:

He did with Buddhism in India what Emperor Constantine did with Christianity in Europe and what the Han dynasty did with Confucianism in China: he turned a tradition into an official state ideology and thanks to his support Buddhism ceased to be a local Indian cult and began its long transformation into a world religion. Eventually Buddhism died out in India sometime after Ashoka’s death, but it remained popular outside its native land, especially in eastern and south-eastern Asia. The world owes to Ashoka the growth of one of the world’s largest spiritual traditions.

Answer 2

The reason this was possible was because post Alexander, the Greek rulers of conquered territories got local leaders to accept their political dominance by taking on "local coloration," that is, adopting local customs and religious practices.

An example of this is the so-called Selucid Empire that dominated Asia Minor. The "culture" section of the link described how this came about.

In Egypt, the Ptolemaics became "more Egyptian than the Egyptians," even going so far as to adopt the local practice of royal incest (Cleopatra was forced to marry her younger brother).

Likewise, in India, the Greeks that reached the outer limit of Alexander's conquests "fused" with the locals, initially called "Bactrians." JAsia has produced a better answer about how the "conversion" to Bhuddism actually took place, but the important thing to note is that the Greeks (generally), were open to such conversions.