We have a house in SW france with 3 large beams running through the bathroom -- they're about a metre above the shower head. There's an exhaust fan, but no VMC system. The bathroom has been in place for about 30 years, since the old stone house was renovated. I worry from time to time that this is "a bad thing", but the massiveness of the wood seems to take the extra humidity in stride. They seem to be doing fine, no obvious signs of mould, weakness, etc. I'd say, in your case, go the VMC, keep the beam uncovered, and poke it with a skinny screwdriver from time to time to make sure it's solid.
Q