I think your best bet, muzzlet, is to chop the celery and put it in containers in the freezer to use in cooked dishes and go out and buy another bunch of celery.
I always keep several bags of chopped celery in the freezer to use in soups, stews, stuffings, and other dishes that call for quantities of chopped celery.
I don't really know of any way to remove the bitterness. Just buy more celery and hope for the best. Although, the "heart" of the celery should be sweeter. Maybe you can salvage that.
"As a girl I had zero interest in the stove." - Julia Child
This is real inspiration. Look what Julia became!