Probably not. The Bella Vista trails are single track, well engineered trails, but the natural terrain is pretty rocky and cherty. A street bike is going to have a lot of tire troubles on any of NWA single track trails. There is a paved, skinny tire friendly 37.6 mile Razorback Greenway Trail that runs from the Bella Vista Trail in North Bentonville through Bentonville, Rogers, Fayetteville, and more. The far northern section through Bella Vista will open soon.
In addition to a bike designed for off-road mountain-biking, you will need additional safety gear. Even on beginner an intermediate trails, it's a lot different than road riding. There are sources of expert advice on how to outfit yourself and your bike for NWA mountain bike riding. Local bike shops are familiar with NWA trails and can be trusted to give you good advice. If you aren't sure mountain biking is for you, you can rent a mountain bike that will give you a fair and successful experience before investing in a bike of your own.