Final answer:
The spread of Buddhism over the Silk Roads was mainly due to the efforts of the emperor Ashoka's missionaries, monks, and merchants, with Ashoka's conversion to Buddhism playing a pivotal role in promoting the faith throughout Asia.
Step-by-step explanation:
The principal agents for the spread of Buddhism over the silk roads were missionaries of the emperor Ashoka, Indian monks, and merchants who traveled these routes. King Ashoka, after his conversion to Buddhism, used his power to promote the faith widely, including sending his own son as a missionary to Sri Lanka. Later, the Kushan Empire's sponsorship of Buddhism and the traveling Buddhist monks, such as Lokaksema, helped further propagate the religion along the Silk Roads, reaching out to different regions including China.
Through the Silk Roads, monasteries were established offering places of rest and worship for travelers, thereby aiding the spread of Buddhism. Notably, small oases such as Yungang greeted weary travelers with grand religious symbols of Buddhism, and monks played a pivotal role in translating and spreading Buddhist teachings.
Ashoka's conversion and support of Buddhism were instrumental in its proliferation across Asia, and were further carried on by traders and monks who navigated the complex trade routes, embedding Buddhism into the cultural landscapes along the Silk Roads.