It is more unlikely to have altitude sickness in Bhutan than most other high-altitude areas. There are two reasons.
First, most tourist attractions in Bhutan are located in the middle area of Bhutan, where the altitude is between 2000 meters and 3000 meters. As you may have known, most people will have altitude sickness only when they are in areas, where the altitude is over 3000 meters.
Second, the percentage of forest cover in Bhutan is over 72.5%. So, the oxygen content in air is higher than most other high-altitude area.