If you dont want to use chemicals... We have a huge tick problem and my youngest daughter has lyme, After she was diagnosed i went on a rampage and ripped out 30 apple trees around the house, cleared out all the brush/logs laying around, Got rid of any wet spots. Put up Loads of Owl Boxes, Set large stones around for foxes to use for sighting prey and use mouse buckets (five gallon pail with water in the bottom and a spinning can with peanut butter at the top) you have to make them coon/skunk/bear proof around here though. I also just step on the Voles when i see them running around.
We still have a lot of them though and ive only begun my seng journey a few years ago so I cant really say if they are in my beds yet.
Do you have to dig up the roots to tell if they have been chewed up or can you just look at the bed and see the signs of rodent festivities?
I'm having vole issues this year as well. Since the cats like to catch them, I don't use pesticides like I would normally suggest. I've tried the 5 gallon bucket and it doesn't work at all for me. The best way Ive found to catch them is use a regular mouse trap and find their runs right under the straw, then bed that trap in where they run across the trigger when they come through.