Put the water, salt, sugar, bay leaves and peppercorns in a pan, over a medium flame and warm until the salt and sugar have completely dissolved.
Remove from the heat and allow to cool.
Add the vinegar to the pan. Wash a jar with very hot water and in a warm oven so it is sterilized.
Peel the turnips (and beet), then cut into 1/4 inch wedges.
Put the wedges in the jar, cover with the liquid.
Seal and leave for at least a day and up to a week.
Once opened, store in the fridge