People.
People who didn't want things to change who were afraid of following another faith simply just people.
Mainly reason, logic and good sense.
There is ONLY one kind of Buddhism in this universe. Since Asoka is an Indian he practised Buddhism with Indian culture. Asoka was a king and therefore had the power to spread Buddhism by building many places where Buddhists can performed the way of life.
Cultural difussion
Diamond Way Buddhism was created in 1972.
It was spread by Buddhist Monks during the reign of King Ashoka of India, in the same way that Christianity entered Europe from Israel/Palestine.
As a Buddhist emperor, Ashoka believed that Buddhism is beneficial for all human beings, as well as animals and plants, so he built a number of stupas. He also well spread Buddhism to neighboring kingdoms.
I think you mean the Silk Road, a trading route and pathway for cultural transmission that extended from China all the way to Egypt and into Europe.
A young leader wanted to find the best way of life, he sat under a tree starving until he found the answer to his question, he carried followers which started missions to spread the religion.
It is the other way around. Buddhism was started by a born Hindu prince. Many Gods and Goddesses from Hinduism are used in Buddhism.
Buddhism does have organizations mostly in the way of monasteries. They don't have missionaries as such but monks do got to places where there is an interest in Buddhism.
A young leader wanted to find the best way of life, he sat under a tree starving until he found the answer to his question, he carried followers which started missions to spread the religion.
Buddhism isn not really a religion. it is just a way of life.