It kind of depends on what has settled into your paint. Each situation may be different.
Sometimes, if it is large, you can grab is with a sharp pair of needle nosed tweezers whil the paint is still wet. If needed a light spray with the airbrush after picking it off and you're set. Usually though, I find that it is more likely to cause harm by removing any dust particles while the paint is wet.
After you let the paint dry, you might be able to still pull the dust off with sharp tweezers, especially if it is a hair or fiber. If the particle has been painted over, you might be able to carefully scrape it off down to the level of the surrounding paint with a sharp No.11 blade, and/or lightly sand with 600 or finer sandpaper. After andy repair work, you may have to touch up with a brush, in which case use highly thinned paint to avoid brushmarks and build-up in the middle of an airbrushed surface. Clear overcoats and weathering will help hide any blemishes caused by the repairs.