Buddhism spread outside of India
Hinduism and Judaism were historically not that intent on evangelism. Both these religions have more cultural/ethnic roots. Like the pagan religions of Europe & the religions of China, the missionary zeal was absent. There is nothing in the religious texts that makes it a duty of the followers to spread the religion.
On the other hand, Buddhism, Christianity and Islam were designed to be evangelistic and founded with an explicit desire to "root out" the existing practices. Their followers zealously took into their head that they found a secret that they want the "ignorant world" to know about.
Hinduism also lacked the equivalent of Emperors Ashoka and Constantine who respectively spread Buddhism & Christianity through a massive empire. These emperors also sent their missionaries all over the world, carrying the religious message. Islam was aided by the swords of Arab and Persian empires and later the Ottomans. Although Raja Raja Chola and Krishna Deva Raya did their best to fight for Hinduism, their empires were not that big.That said, Hinduism at one point was all over South East Asia. You can still see the remnants of that rich culture in the Hindu temples of Bali and Angkor Wat. Kings of Thailand are named "Rama", Laos is named after Rama's son (Lava) and Indonesia's national symbol is the Garuda.
Outside of South East Asia, we have countries like Mauritius, Guyana, Fiji, Suriname and Trinindad where Hinduism is a dominant religion.
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Buddhism is a religion born in ancient India in which meditation is a central tenet.
Who was the king that spread Buddhism in India?
Ashoka was the Indian emperor (reigned 272-236 BCE) who embraced Buddhism and spread it in India and Ceylon.