A nuclear waste reprocessing program should be 100% government run, or at least government controlled, because part of the process involves refining the plutonium that could then be used to make nuclear weapons. This is why most countries don't reprocess their spent fuel, it's considered a nuclear weapon proliferation risk to reprocess, and the downside of accumulating spent fuel waste is considered minor in comparison to the risk. Buying spent waste from neighbors would be unexpected, because (a) waste reprocessing is more than self-sufficient, and (b) there's not much in the way of transportation infrastructure because countries are extremely cautious not to lose track of spent reactor fuel due to proliferation concerns.

The reason for not dumping it in the ocean is exactly as stated above. It's extremely valuable, in large part because of the plutonium content, and it's senseless to throw away something so valuable that the nation may eventually have a need for.