I agree with Bill that an uncovered compost pile (or bin)
should be fine as long as you use a sufficient amount of
straw layering on top each time the
bucket is dumped. This not only provides good drainage, but it allows air into the pile to help in composting. We have historical average rainfall of +50" here (this year seems a lot higher right now) and even with that the compost bins become dry and need watering. We've been using the Joe Jenkins
Humanure system for over 3 years.
One other comment because I have seen this stated incorrectly before on this forum ... Joe Jenkins does NOT have a roof over his compost bins. His system has two uncovered bins separated by an area with a roof where he stores his straw. The roof is also for rainwater collection used to clean the buckets, not necessarily to water the compost.
We made our bins using reclaimed wooden shipping
pallets (approximately 4' x 4'). Try to find heavy ones that have the boards close together. These are normally used for shipping cement products and they make great walls for compost bins.
Good luck with your home building
project.
-Tom