Storing in the bathroom is not a good idea. After use, I dry the razor, lightly oil the blade and pivot and then allow it to sit in the open air on a shelf in my bedroom for 24 hours so any moisture on the scales can evaporate. Remember that moisture affects not only the steel blade, but also scales made from natural materials such as celluloid, wood, or horn. Plastic, laminates, and bone are less likely to be affected.
I store my razors in a Plano storage box. The box can go on a shelf or in a drawer. The box I use is:
https://www.amazon.com/Plano-23705-0.../dp/B000E39T5U
It should be available at a local store as well. Look for Plano Prolatch model 3705, 4-16.
It has four fixed compartments and then comes with dividers that can be used for storing smaller items; but for standard size razors, the fixed compartments are perfect. Unfortunately, I have a couple of oversized razors that are too long to fit, so they go in leather sheaths.
In the winter, the air is sufficiently dry in Chicagoland so humidity is not an issue, but in the summer, I may add desiccant packs to the storage box.