The info provided by Astrophsx is spot on and matches my experience.

I was only there for a few days and had a lot of bad weather so I don't have much to add, except to offer reassurance that if you want to visit independently then it is very much achievable with little difficulty.

My hotel airport transfer was $6, but that's in a cheap local hotel not an international chain.

Kona Bikes have good quality bikes for $35 per day, and I rode around quite freely without ever needing a guide. If you enjoy cycling, then cycling is a great way to explore and see something other than the endless temples and monasteries (especially if you enjoy going uphill in the rain for 5 hours, and then freezing as you come back down in 45 minutes...)

Only one out of the three ATMs I tried would accept my card, and there is a fee to withdraw.

Alosim and Airalo e-sims worked for me, though it did take a while to get connected and the data speed is very slow. Alosim seemed to work more reliably.

I did not need a guide for the Tiger's Nest hike, but you do need one to go inside the monastery.

Travelling independently in Bhutan is easy and cheap, though I did get the impression that taxi drivers and many restaurants are not used to foreigners other than when accompanied by local guides, so a little patience and perseverance to overcome the language barrier was often necessary.