I did it when I was backpacking Vietnam (maybe 7 years ago now, so I think its probably more busy now) - we used whats called an easy rider, so didn't ride our own bikes and had a local ride instead and we sat on the back. My driver was really nice, calm and I felt safe.
There was one girl there who has never ridden a bike before but decided to ride one herself, and she fell (not badly) around 3 times because she was struggling to keep up round some of the windy parts.
But if whoever is going has some experience riding bikes already, then I think its pretty safe to ride your own - with a helmet of course.
It was insanely beautiful, FREEZING, and one day was so foggy we couldn't see anything. I have never drank much so didn't there either, but the local alcohol they give you is very strong - I think probably 60-70% so be aware of this if drinking.
Overall would recommend, its a fun experience and don't be scared by the news of the teenager dieing. Hundreds of people pass through there everyday so ofc there will be accidents, same as driving on the roads here.