I've been hunting for the actual law that banned television but it's proving elusive. I'm not sure I'll be able to find it without being in the country. It's very possible that it was passed under royal decree as television was banned (most likely) in the 1990s as pressure for Bhutan to modernize, Westernize, and democritize was increasing, all tied up with the Nepali troubles.

A series of laws were passed between the '70s and '90s to try and protect Bhutan's cultural heritage. These included strict immigration reforms aimed at protecting the delicate demographic in the Himalayas that had recently toppled Sikkim (the King of Sikkim was the uncle of the King of Bhutan).

My understanding is that banning television was motivated by the same desire to control the balance of modernity and tradition that was rapidly changing Bhutan's neighbors. All they had to do was look at what was happening in Tibet, Sikkim, Nepal, and India to see that modernization wasn't all it was cracked up to be.

I'll admit that I'm technically deficient, which makes untangling the puzzle a bit of a mystery to me. The Bhutan Broadcasting Service (BBS) was started in 1973 as a government-sponsored radio program and expanded in 1999 as Bhutan's first television channel, indicating that the ban on TV was lifted at least before the turn of the millenium, though that's skirting the 20-year rule to discuss it any further.

The most obvious explanation, though I'm struggling to find primary sources, such as a royal decree, is that banning television was just one of many measures taken to preserve Bhutanese culture. Other measures taken included a national dress code, the implementation of Dzongkha and English as national languages, and strict immigration and tourist policies.

[Side note: Most television media today comes from India. BBS owns at least two television stations with most of Bhutan's Dzongkha language media, but the rest of their programs come from India, which leads to the weird phenomenon of the children all being able to speak Hindi because there's no Dzongkha language cartoons.]