How do I clean up white dust and spots "blooming" on rubber?
One of the most common solutions to rubber bloom (in pretty much any setting) is an interior car cleaner like "Armor All" (not an endorsement, just an example). This is a durable oil-based product that is less volatile and less likely to be removed by friction or otherwise.

I typically only have to re-treat the weather stripping in my car 1-2 times per year with a product like this, and it keeps them from cracking, blooming and otherwise deteriorating as fast as they might otherwise.