You should really seal them in something air and bug tight to prevent molding and insects from getting into them. I would think that a good brand of commercial rabbit pellets should have a best before date stamped somewhere on the packaging, or at least a date they were manufactured... and they can vary in how long they last depending on what is in them. I don't think they'd last much longer than 6 months, to a year at most, before much of the nutrients were depleted and they became dried out and unappealing. My rabbits are fussy, but eat like pigs so pellets don't last long around here.
When I used to have several rescued rabbits I needed to buy the huge bags of pellets from the feed dealer.
I found that storing the pellets in a few medium sized "Rubbermaid" type of bins helped keep them fresh.
This way, only one bin is opened and used at a time leaving the others sealed and not exposed to air/humidity etc.
I would rather keep it in a sealable tote box rather than a garbage bucket. Bugs and animal pests have no problem getting into a garbage pail.
How many rabbits are you keeping?? And is your basement free from mice/rats/spiders/carpenters/earwigs etc??
Even in a sealed tote I notice the color is gone out of the pellets when it's time to buy a new bag (about a month) bc it's opened everyday. So I would never keep more than a 2kg bag at one time.
I don't know how much freezer space you have, but when I buy pellets in bulk I keep about a months supply out in an easy to access air tight food storage container. The rest I seal up also in air tight containers and store in the freezer. In my experience that helps to keep them fresher for longer, but I know not everyone has space to store a bunch of rabbit pellets in their freezer!