I have used fresh clean straw under mine before. However, I also have problems with field mice in the winter time having the straw in there. It attracts them for a good nesting place. So ..... maybe someone else has a better idea. But straw is what I had been told to use.

Pine needles! I'm lucky enough to have a neighbor with dozens of pines trees and he's kind enough to rake them into piles for me to collect for the garden. Pine needles are airy and tend to dry out faster than other mulches which makes for an excellent base for the berries to rest upon. Also keep weeds surpressed and hold in soil moisture.