I think using noise in bump map here is not the best way to achieve real noise.
Just as Maru righly said, this material in real can be polished, hence it won't have surface noise, and this noise is so microscopical on the underneath brushed layer, that better would be to
use noise or texture on specular level.
I like the idea of blanding two layers, metalic underneath with gloss and lower reflectance and upper polish (IOR based) with high reflectance and low-gloss (mirror-like reflection).