Many bearings are commonly available in stainless (440C). I suspect that will be fine for the duration of training. Plan to replace them before the competition, and don’t worry about it. You could try to seal and pressurize them, but that’s just seal drag and probably not worth it for a one off.
Some of the plastic bushing companies used to sponsor those competitions. We never used them the the ASME bicycle competitions due to drag concerns, but they won’t corrode.
If you want to learn something interesting look up the designs behind the wet wooden bearings used in power plant turbines and at least one early nuclear submarine.