Depending on the material (Natural vs. Synthetic) there are a few approaches you might take. It sounds like you don't actually have to show the bullet hole happening on film, just the aftermath. Is that correct? If so, here are my suggestions. If the film quality is low, like digital video or something like that, then just do the effect with paint. You can cut a hole in the shirt and then airbrush the powder burn around it. You could also dry brush it with a fan bristle brush of you don't have an air brush.

If the film quality is really high, like 8 or 16 MM, you would probably do best by actually burning a hole through the shirt with a soldiering torch that you buy from a hardware store. Have someone close at hand with a spray bottle or bucket of water for this. (Don't use a fire extinguisher because you'll never get all of the white foam out and that will show up on film.)

Maybe the easiest solution of all time though is to just use a lit cigarette to burn a hole in the shirt and then rub some of the ashes into the area around the hole. The Ciggy is about the size of a 9MM bullet hole and the ashes would be the right color. Powder burns at close range tend to look a little like tiny, hot buckshot hit the object. For that you might try Heating the tip of a nail red hot with a torch and carefully stippling the area around the hole with tin y burn marks.

Hope this helps.