In a trip to Key Largo with 20 dives in 2013, I saw a few Caribbean reef sharks (I think nurse sharks, too); the reef sharks were skittish and the Rainbow Reef Dive Center guides had little mirrors, which they held out and wiggled (I think to create the shiny moving look of a thrashing fish). They weren't numerous and tended to keep a distance or move on.
The Bahamas and Turks & Caicos (the Caicos area; I don't know about Grand Turk) have a rep. for Caribbean reef sharks. I've been to Turks & Caicos via live-aboard, and yes, we saw some. That works. I've read Stuart's Cove does baited dives with reef sharks, but you can see them without baiting in the Bahamas and T&C.
In the Caymans (2016) and St. Croix (2017), Caribbean reef sharks came around us at a slower pace, closer, made some passes, and I took this to likely be a hold-over from past shark feeding. A guide in St. Croix told me the reef sharks used to be deeper, down around 90 feet, but people fed them lion fish and they started patrolling shallower reefs. People quit giving them lion fish (from what I understand), but when I was there in 2017, it was a good place to see reef sharks pretty close up without feeding. I saw them in 2015 while live-aboard diving out of Belize; a couple made life interesting for a guide carrying a speared lion fish, and on one dive one maybe 5 feet long entertained us on a baited dive (dead lion fish in a perforated 5-gallon bucket).
Saw nurse sharks and some small black tips (I believe they were) in Cozumel in 2018, but the black tips aren't a reliable thing.
My point is, if you want to see Caribbean reef sharks without baiting, there are a number of places you can go with good odds if you do a bunch of dives.
One place at this point in my life wouldn't go...oceanic white-tip diving near Cat Island in the Bahamas. I don't know whether they bait or not. I've read about diving with a few of those sharks...too rich for my blood.
Richard.
P.S.: I am not inclined to try the 'waving the mirror' and similar tricks. An article in Alert Diver online,
A Shark Tale, by Mary Maguire, describes a reef shark incident:
"Art had just speared two lionfish and was heading back to the boat when he attracted the attention of a couple of 3- to 5-foot-long Caribbean reef sharks. They were drawn by the fish blood and dying movements of the fish on the end of the spear. One shark swam up under Art as he made his way toward the boat. As the shark opened its mouth and headed toward the fish, he encountered Art's left hand instead. Art says it was sudden, unexpected and painful. He tucked his fist under his right armpit and continued to the boat, where he handed up his fish. Sue and Paula then helped him aboard, applied a pressure dressing and helped him remove his suit. There was a lot of blood. Art doesn't remember any of this."
As long as there is no food in the water, or I'm not holding it, I don't worry about reef sharks.
Here's a video showing a diver rubbing a bottle on a very deep dive in Papua New Guinea, another trick to draw sharks. Well, it
worked...