Bloomberg's source for the information asked to remain confidential, but we can confirm part of the information: BMW applied for a trademark for "Access by BMW" on March 20, 2018. The use case covers "Vehicle rental services featuring a monthly subscription service providing vehicles to members for their personal use; vehicle delivery services namely, delivering vehicles to members of a monthly subscription service."
That BMW would choose Nashville for a test location comes as a surprise. Porsche unveiled its Passport service in Atlanta, GA, site of the company's U.S. headquarters. Cadillac rolled out its Book service in New York — the carmaker's HQ — Dallas, and Los Angeles. Volvo's Care by Volvo program runs nationwide, and it sounds like Mercedes-Benz will go for broad coverage when its Flexperience scheme debuts at some point this year.
The Bloomberg report said Access by BMW would "be offered by a local BMW dealership in Nashville," but there's only one: BMW of Nashville. That location earned BMW's Center of Excellence award for 2016. Otherwise, we can't find an obvious reason to nominate Tennessee. And that might be the point — working with a single dealer in a contained, manageable market. Assuming Access by BMW launches this week, we should get a lot more details, such as available vehicles and pricing, shortly.