Not sure what kind of worm is infesting your turnips, but if it is root maggots, the crop can be protected in the early spring with floating row covers - flies lay eggs in the soil, their offspring (root maggots [they become flies later on]) hatch and start feeding on roots. If you keep the flies away with floating row covers they can't lay eggs in your soil.

I have also heard that a mixture of ammonia and water in a squirt bottle can be applied around root vegetables to ward off root feeding pests. I haven't used ammonia and water myself, so I can't say if it helps. Good luck.