I would chop them up in a food processor and just watch until they were a good size. Look I'm no expert on Bolognese, but I frequent a
restaurant who does very good Bolognese and you never ever see the vegetables in it. They're supposed to be cooked in. And the meat is supposed to be very soft by the time it's done. So I would think a food processor just chopping it right on down there would be perfect.
The other time I really process vegetables is onions going into meatloaf. Chunky onions just breaks meatloaf apart.