I'm sure your scope will work on your rifle. Where did you hear that this scope wasn't recommend for use on a WSM rifle?
One disadvantage that lower end scopes like the Bushnell Banner scopes may have is limited eye relief. No one likes Magnum Eyebrow! I don't know the specs for your specific scope, but it might be something to watch for.
There's not really any reason that your scope won't work for you. There is some truth to the saying that you get what you pay for though. If you compared your scope to a higher end scope side by side you would probably notice differences in clarity and brightness, especially at times when it's darker outside. One of the most common recommendations I see on this board is to buy the best scope you can afford.
I don't think that you have any reason to expect any problems though. At one time I had a 4 X 12 Bushnell Banner scope on a .222 and I used it for several years without any problems. Eventually I bought a better scope when I could afford to though, but the Banner certainly worked.