We've got a large ornate (~12") in with our rays, and he hasn't bothered them at all. We watch him, of course, and observe the rays closely every few hours. I've seen a video (posted here, somewhere) of tiny pups crawling right over a gigantic bichir and they seemed to be getting along really well.
Stingrays + bichirs can be an awesome combo, if you observe them closely (especially in the first few weeks) and make sure the dragon eel gets his share of food. Healthy stingrays are voracious eaters, and bichirs are almost blind and have trouble getting enough food; this is especially the case when you feed small amounts infrequently, but it can be relieved by more infrequent, large feedings or simply by distracting the rays with food in one part of the tank and sneaking the little bichir some food while the little vacuum-cleaners are busy chowing down.
Also, something to be aware of is that bichirs are often bottom dwellers and will reduce the footprint available for the rays. They are also a bit messy, so if you are going to add one know that it will noticeably reduce the capacity of the tank to house stingrays.
Hope this helps, and best of luck.