I visited this area in the northern summer of 2019.
These gardens were the first created in Bhutan, and they were opened in 2008. Inside the main accessible central area at the gates, there is the Rhododendron display, a lake, lots of large trees, flowers, and walking tracks, over an area of 50 hectares. However, the park actually extends for another 120 square kilometres between surrounding national parks, and includes the viewpoint and stupas at Dochula Pass.
As with a lot of nature watching in Bhutan, it is often best to simply walk along the roads that wind their way through the mountains. The road leading down to and around the gardens is good for birding.
You might also spot the occasional Pika in the undergrowth...
For more places to see wildlife in Bhutan.