You got me curious, so I did a bit of googling around.
I found a bike club, although the website is out of date: http://www.shreveportbicycleclub.org/
I found a blog that mentioned a Critical Mass Ride in November: http://redriverblogjam.blogspot.com/...e-ride-in.html
I found that evidently, there was a Tour de Goodwill held there last May, although I don't see info for a ride for this May on the website. Going to mapmyride may locate the Tour route, though.