Hammerite is an option, but what I would use is a primer product called Galvafroid which is extremely zinc rich becoming well in excess of 90% zing on drying out. This is sometimes referred to as cold galvanising. Make certain the bucket is clean and dry and apply this product by paint brush all over the inside, concentrating on the joint(s). Do that in two coats - you need only to minimally prepare the surfaces for the first as you can go right over rust, as long as it is light (otherwise wire brush the worst off and wipe all the dust away). Note that white spirit is not likely to work for cleaning the brush so use something like aluminium foil to wrap the brush to stop it from going totally hard between coats - or else buy two cheap brushes with the aim to throw them out afterwards. Let the first coat dry for at least 4 hours in a well ventilated location..