Wood shavings are not good at all for wooly buns. I have a very wooly teddy lionhead bun, I use paper pellets in his litterboxes. Paper pellets can be used as bedding too, but it’s quite practical to litter train your buns, and the material in the litterbox should not be the same as in the living space.
In my buns living area (he’s free roam but he has his own favorite cardboard houses etc) I have fleece blankets cut into manageable pieces as bedding. He likes to dig in them and they’re easy to wash. I buy the cheapest ones I can find because they will get many holes in them and they will be washed often, so no use getting anything fancy.
The fur of wooly rabbits is as a rule “worst” before the bun has got its adult fur coat. This happens around 6 months to a year. Before that you should preferably brush the bun daily to avoid getting bad tangles. When the adult fur comes in, you can as a rule cut down on the brushing to once a week.