Are there any studies concerning how many wild bee colonies there are in US?
I mean really wild, not swarms.
Since the decision to assume that there were no native honey bees (no new evidence was found, but people were tired of the conversation I suppose) all bees in North America have been labeled as "feral". So there are no wild colonies in the US. If you mean feral colonies, according to Thomas Seeley's work in the 1978 and again in the 2015 the density of feral bees in Arnot Forest is the same now as it was then. His survey showed a density of about 1 feral colony per square km. (1.06 to be exact) both in 1978 and in 2015. Genetic testing shows they are not closely related to the local domestic colonies.
I don't know of published studies on the topic. Everywhere I go I find feral bees. While some people insist there are none, I ask other people in the same area and find they have been finding them.