Presume yours is the old type root chopper that is worked by a round plate like a vertical flat grater?
Well after all our wide necked catching containers had rotted away, I found a simple solution. This was to use a large bucket on a breeze block, or similar. The block raised the bucket right up to the throat of the chopper, so the bits of turnip went straight into it as they didn't have room to go shooting all over the place. This also has the added advantage that your catching container has a handle, so you can carry 2 at a time.