If where to shoot includes a membership based Club , Berwyn Rod& Gun is IN Bowie. And a fine club. The dues structure amortizes out if you shoot regularly, but could be steep if you only shoot a cpl times a year.
For commercial , pay as you go ranges, On Target is north in Severn. Md Small Arms is south in Upper Marlboro ( think closer to Forrestville).
Gun stores you'll probably want to roam the larger metro area . The specifically closest is Worth A Shot in Millersville ( north on Rt 3).
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Berwyn, where I'm a member, is by far the closest place to Bowie to shoot. See http://www.berwyn.org. It's also the nicest, friendliest group of people you'd ever hope to meet, though membership is certainly expensive. The general membership meeting is at the DAV on 197 at 7:30 p.m. the first Wednesday of each month. You should swing by on June 7. Visitors are always welcome--and we have pizza at each meeting, which should be enough incentive to get you there! Send me a PM and we can work out a way to meet up on June 7.
A1 Uniforms, on Volta Ave. in Brentwood, is a store that's also pretty close to you. They used to be an Industry Partner here, and maybe still are. They were also talking about moving last time I visited, which was a few months ago. So you should double check the location. Good folks.
If you don't mind a bit of a drive around the Beltway and down 95, Sharpshooters in Lorton was nice the one time I was there last summer.