Sweet Melody, Fairhope and Snow Bride are a few good ones. Hard to beleave but white mini's are hard to come by.

If you can find it, I've also had good luck with Irresistible. It will need to be treated for black spot, but the blooms have a great shape.

To me the best white mini is Irresistible.
You might look at Memphis Queen or Cape Hatteras.
Fairhope is not white, it is a light yellow according to toe American Rose Society.
Also if you can find it Sandy Lundberg

Thanks for your suggestions!