Common sense dictates that with India's strong military and tolerant attitude toward Hinduism's sister religion, Tibetan Buddhism (as well as other religions in general), dharamsala would be an ideal place to exile safely from China. There is a very large number of elite soldiers guarding that hill station, as it has been heavily fortified against Chinese incursion for a long time.

Nepalese, Bhutanese ability to defend against a much larger PLA would be fractional at best.

Hi there! I am away from my personal library where I could access Tshering Shakya's The Dragon in the Land of Snows, the most comprehensive and detailed history of modern Tibet. It includes this very issue which I can only give my most basic summary here, but I encourage you to read it if you're interested in this topic.

Bhutan, first of all, had no recognition from the PRC. At best they were considered a begrudging client state of India, at worst they were considered a fractious portion of Tibet (which the Chinese now claimed to be the sole owners of) so Bhutan was a messy, unclear situation that may or may not have resulted in invasion and war between China and Bhutan.

It was after the invasion (I don't have the timeline handy, so check out the book, or Karma Phuntsho's The History of Bhutan) that Bhutan and India signed mutual defense agreements mainly aimed at any further Chinese landgrabs against Bhutan.

HHDL knew that India and China were becoming closer to try and stem their reliance on either the Soviet Union or the United States, so while his initial reaction wasn't to drive a rift between the countries, it was clear and obvious that India at least was recognized by China and they would think twice about invasion. However, the Dalai Lama was well aware that Nehru could have asked him to leave India, in which case there were plans to lead the resistance and exile effort in Sri Lanka, and failing that, Thailand. The idea being that the closer they could stay to Tibet, the easier it would be to return.

When it comes to cultural differences and similarities, Bhutan and Tibet are similar to, say, Spain and Italy. Shared Latin and Catholic heritage? Yes. But the religion and (obviously) language are incredibly different and history itself has been contentious. Bhutanese are not Tibetans and there are many Tibetan cultural norms (for example, ending elders' names with the suffix -la) that are not normal or can be even insulting to Bhutanese (who will only end questions with the honorable suffix -la). Tibetans follow the Geluk School of Vajrayana Buddhism, which is only found in Bhutan's far east among Tashigang Merak and Sakteng herders (the Dalai Lama is the de facto head of the Gelukpas, while the Ganden Tripa is the de jure head). The Bhutanese are followers of the Kagyu School (for the most part, largely concentrated in the western half). And while these things are of no concern to common Bhutanese (Tibetan store owners will proudly display an image of the Dalai Lama in their Thimphu shop, and Bhutanese customers will pay it due respect) it's important to note that it is considered a cultural difference and Bhutanese would not be particularly sympathetic to the Dalai Lama's plight. The seven wars that were fought to separate Bhutan from Tibet had their origins in the Gelukpa-Kagyupa conflict that saw many people flee to the southern Himalayas, including to Mustang in modern Nepal, and Ladakh in modern Kashmir. The founder of Bhutan, the Zhabdrung Ngawang Namgyel, was one of these refugees.

After the Dalai Lama's exile, thousands of Tibetans followed him. Mostly through India and eventually to Dharamsala, but many Tibetans went to Bhutan. This initiated an unfortunate series of events, including an idea that the Tibetans might not culturally assimilate and the King of Bhutan might face difficulty ruling over those who saw themselves as foreigners, following a separate king (prince-lama is the common academic term you see more and more of) and even considered themselves of a different school of Buddhism. It's discussed in Omair Ahmad's Kingdom at the Centre of the World how the King of Bhutan issued a proclamation that asked all Tibetans to either culturally assimilate (learn Dzongkha, dress in Bhutanese ways, etc.) or leave Bhutan for India where there were many Tibetan enclaves (Dharamsala was by no means the only one, Tawang was still under Tibetan control by the time the Dalai Lama escaped, and it was briefly considered for the exilic base). Tibetans living in Bhutan pretty much en masse followed this order: many assimilated, and many left, and it was a pretty peaceful transition. When the King of Bhutan made the same request of the Nepali speaking Lhotsampa, it didn't have the same result.