My name is Joan and I have been a Vet tech for 30+ years with special interest in Bearded Dragons.
The Betadine soaks will not work unless used in conjunction with cleaning the tank with a bleach and water solution, disposing of all cage furniture and treating the surrounding areas. Mites are hard to get rid of and you have to be persistant to get rid of them. When bathing the Dragon in the Diluted Betadine Solution, you need to use a soft toothbrush to gently help to get the mites from the scales. The Dragon should be on paper towels during this process. There are products on the Market to help get rid of mites, but all are toxic to Dragons. Since you have just purchased this Dragon I would go back to the store and lodge a complaint. The Dragon had the mites at the store and should have been treated before you purchased it. This is a link about treating mites: http://www.anapsid.org/mites.html
There is a medication called Ivermectin, but I would never used it. I have seen it kill Reptiles when used for mites. Please let me know if you have further questions about the information. Joan