I finally figured out how to make them so they weren't too watery.
The turnips were an annual Thanksgiving dish in my DH's family, so I didn't start making them until I met him. His mom cubed them and cooked as you would potatoes. This method didn't ever work quite right for me.
This year, I roasted them in the oven - whole and wrapped in foil as a potato. I ran them through the ricer, added butter and cream and a pinch of salt, and mashed with a fork. Heavenly!