NO - pine shavings and needles are not recommended for rodent bedding, nor are cedar shaving anymore. Only hardwood shaving, aspen being the most common are recommended. Or recycled paper. Pine and cedar(a conifer) have phenols that can cause the liver of your pets to shut down just from breathing too much of it. *Rabbits in the wild never girdle/chew pine trees.Does it have to be hay?
If it's not going to fall through a screened flooring, would a bag of something like this work? We use them when we go to horse shows, or at camps where you have to bring your own shavings to a stall.
https://www.farmandfleet.com/products/595378-guardian-horse-bedding-premium-pine-shavings.html?
It would also keep the car & where ever you store it cleaner.