I've never been to BMS.
Seems like I have heard others say they have carried with no problem, but not sure if I would or not.
If the government owns the speedway it could fall under 39-17-1311 which prohibits carry and Public Parks and Recreation areas
Also TN prohibits carry within the confines of a building that sells alcohol for onsite consumption...which I'm pretty sure you can get a beer at BMS
And any place can post a sign per 39-17-1359 and make even their parking lot off-limits.
But as far as searching your vehicle and or person, I can't help sorry.