The mite wash (alcohol or Dawn dish soap) and sugar roll test are both quantitative measures of mites. They tell you how many mites per 1/2 cup of bees (300 bees). It's very possible to do the sugar roll test without killing bees. It's also 90-95% accurate if you shake hard.
The thing that kills bees with the sugar roll is if the bees get sticky. If you keep the bees dry, it removes mites and keeps them alive. Randy Oliver did a test a few years ago and none of the sugar rolled bees were pulled out of the hive. I see them getting half cleaned off in half an hour, and probably fully clean in 1-2 hrs. To prevent stickiness, I use extra sugar (1/4 cup rather than 2 TBSPs) and keep the jar out of the sun. Overheating can also kill bees/make them sticky.
The sugar roll test is maybe more tricky to get right, so get someone to show you it that has done it for years and kept their bees alive with it. If you can do the mite wash (with Dawn or alcohol), that's a great way to monitor too. A lot of beekeepers I teach cannot stomach killing bees in the mite wash, and prefer the sugar roll. But figure out what works for you!
The mite drop is not quantitative, but does give you a general idea of mites in your hive. One researcher found that it varied greatly by day and that it seemed to correlate with how much brood hatched out in the bottom box each day. The more brood hatched out, the more mites drop. I prefer to do the mite drop sor 24 hrs. If you leave the sticky board in longer, there is a lot more debris on the bottom board and harder to separate out mites. With a small 1-box hive, maybe 3 day wouldn't be too much debris, but with bigger hives, there is a lot.
Lastly, there was a study on the sugar roll test done last year with researchers that always use the alcohol wash (read: they don't know how to do the sugar roll test correctly). Researcher Katie Lee, from Univ. of Minnesota, has been a big proponent of the sugar roll test for years and saw them speak. She told me they really did a disservice to the sugar roll test. The bees that were killed in their study died because they let the bees/sugar get sticky. That's a sure way to kill bees. Maybe the takeaway is that the sugar roll test is trickier to do.
Hope this helps! Take care, Jennifer
Jennifer Radtke
Learn from the Bees