Grit Blasting

Air blasting.

That's right. Get out the good old air nozzle.

Check what material you are using to grit blast with - some are "lower dust" than others. As the others say, airblow after blasting helps, but if you get the media correct (and if recycling, clean between cycles) it will help.

Depending on the shape of your part and your circumstances, running your inserts through an parts washer with a filter may also help. Are these parts held to a cleanliness spec.? We used to go the air-blow route and after a time, you have a gritty mess everywhere.