Hi OP -- could you resubmit this? The comments below are all pointing out that you mean the Bon religion, not Don, and you're likely to just get more of that unless you can correct it. Thanks!
So Bon, usually spelled Bön because that's how it's pronounced in Tibetan (བོན་) is rather controversial. We have a pretty clear image of what Bon is today but if we go back to "original Bon" opinions range from Christopher Beckwith who insists that no such religion ever existed, to Bonpo masters who have written elaborate histories of their religion and biographies of its founder Sherab Miwo.
Simply put, Bon is the word we use to label pre- and non-Buddhist Tibetan religious traditions. Sam Van Schaik discusses the complex story of the etymology of the word in this paper. The long story short is that "Bon" was originally the label used to describe priests, diviners, and shamans in the non-Buddhist understanding.
The word Tibetans use for "Buddhist" is "nang pa," literally "insider" (ནང་པ་). The word for a "non-Buddhist" is rather naturally "phyi pa," an "outsider (ཕྱི་པ་) which is more than a little awkward/insulting because it refers to foreigners, adding a religious element to the national/regional identity of Tibetan self-conception. Bonpos would insist, however, that they absolutely are "nang pa" even if they aren't "sangs rgyas pa," (a much more literal rendering of "Buddhist" which means something more precisely like a Buddha person, སངས་རྒྱས་པ་).
The traditional place of Bonpos in Tibetan history start with Sherab Miwo, who is the founder of Bon religion and spread it in Tibet before the arrival of Buddhism.
When Buddhism first arrived with the wives of Emperor Songtsen Gampo, Balsa of Nepal and Kong cho of China, Tibet was described by his Yijing reading wife as an ogress that breathed evil into the lives of the people and caused them to do evil. Buddhism, according to his Chinese wife, was the key to civilizing the people and influencing them to do good. The ogress was nailed down and stopped from influencing the people by the construction of thirteen temples. The central one, the Jokhang in Lhasa, is the holiest site in Tibetan Buddhism. One was built in what is today Arunachal Pradesh, India. And two were built in what is today Bhutan, one in Paro and one in Bumthang. Songtsen Gampo is usually described as the first great "chos rgyal," Dharma King, of Tibet. Buddhism took its first great step in Tibet, but the society was not transformed.
One of Songtsen Gampo's descendants married a Chinese Princess, Jinzhong, who happened to be in Lhasa when a plague hit China and a crowd of Buddhist monks escaped to Tibet. The Tibetan ministers were none too pleased and tried to get the Buddhists to leave, but Jinzhong took them under her protection. When Jinzhong herself died, the Buddhist monks were forced to leave. Ironically, in this era, the Tibetans seem much more hostile to Buddhism. They happily raided the cities of the Silk Road who seemed to view the Tibetans in the same way the Irish cautiously waited for the Norse to invade. The Tibetans had a tradition of painting their faces red for battle, and this image of them with what looks like blood smeared over their faces has made it into the histories of both the Tibetans who are quite self-deprecating of their red-faced barbarian ancestors, and the histories of Khotan and Dunhuang who viewed the same red-faced barbarians with fear.
Tibet became increasingly Buddhist over time. All the countries surrounding Tibet were Buddhist, so the influence should not come as a surprise. Tri Song Detsuen, Tibet's greatest emperor, is the one who finally made the shift to royally patronizing Buddhism. The Emperor invited the great Nalanda pandit Shantarakshita to Tibet to set up the first Sangha. Shantarakshita made the long journey, and then left because there were forces, demons, and gods that insisted on harming Shantarakshita. He insisted that Tri Song Detsuen should invite the tantric expert Padmasambhava who came to Tibet and performed a series of rituals that bound Tibet's native spirits to the Dharma. This convinced Shantarakshita to come back and begin setting up the Tibetan Sangha, but it was a tradition that would continue to the present day in various forms. There exist a number of mountain spirits, demons, and gods in the Himalayas which were missed by the mantric experts and remain unsubdued and hostile to Buddhism and Buddhists. But more on that later.
Tri Song Detsuen is considered responsible for the "First Suprression of Bon" as he tried to convert as much of Tibet's religious infrastructure as possible to Buddhism. A famous debate took place at Tibet's first monastery, Samye, between Shantarakshita's successor Kamalashila, and the Dunhuang based Ch'an monk Heshang Moheyan. Indian Vajrayana tradition ended up dominating over Chinese Ch'an tradition, and Chinese monks had to either leave Tibet, or convert to Vajrayana tradition.
Like literally every part of this story, this debate is itself under debate. There's a Ch'an document somewhere that insists that Moheyan won the debate, and some evidence that Tri Song Detsuen accepted Moheyan as his root teacher. But Vajrayana tradition ended up dominating Tibet, either way. And it's more than likely that the "debate" became distilled in the historical imagination to a single event deciding which tradition of Buddhism Tibet would end up looking towards.
Tri Song Detsuen's descendent Ralpacan, the third great Dharma King, is well-known for dramatically increasing his support of the Tibetan Sangha (he increased the monastic tax, angering many, especially those who were not supportive of the Buddhists) and then being murdered when his older brother who was passed over in the succession was supported by this non-Buddhist faction, usually identified as Bonpos.
/cont'd