Since I don't have a problem with rust I'm not sure about this but Sweet Melody is by far the best white mini in my garden. I like it better then Fairhope. If you can grow a good Pierrine, you can grow a good Sweet Melody.

...what Ken said. That's because Sweet Melody is a color sport of Pierrine; which, by the way, is one of the absolutely highest rated roses of any category on the ARS rating scale--9.4 when I last checked a few years back.

I'm curious to hear/read what others suggest, too, because I'm always lookng for a good white rose. Linville grows great for me, vigorous like Irresistible, and prolific. It's white with a touch of pink in the centers. In the cool winter months the whole blooms become the palest baby pink, and grow a little larger, to about 2 inches diameter. That's a fun seasonal variation.
When I was forced to evacuate New Orleans for 6 weeks due to Hurricane Katrina in 2005, most of my roses managed to survive the lack of water, but they looked very parched by the time I returned in October. Not Linville; that goofy rose was in full bloom! It's a sentimental favorite of mine now because of that. Haven't got a clue about the Rust factor, though. Sorry.