You can use mylar liners. Regular plastic is porous and does not keep out air.
Place the liner in the bucket, fill with wheat, rice, etc., place some oxygen absorbers on top, heat seal the mylar bag using an iron. Wait until the next day to pound down the lids, because the oxy absorbers will make the liners contract; you don't want the sides of the bucket to suck in.
That’s very useful info, Max. Many thanks.