Is there a bedding out there that my rabbits can't kick all over my floor?

One of my rabbits binkies all day long and kicks up the bedding on the bottom of the cage and it gets everywhere. I get that rabbits will be messy, but this is ridiculous. And yes, their cage is big enough (about 12 sq feet) and they get a minimum of 3 hours of time outside of their cage to stretch their legs, so she's not mad and kicking to be a pest, she's just really happy all the time and makes a huge mess... I'm always sweeping around their cage! Is there a bedding (not litter, I use yesterdays news in the litterbox) that is maybe heavier, or is too large to be kicked through bars that are 1" apart?