First off, Bronze wool doesn't come in 0000 grade, only steel wool does. IIRC, bronze wool's finest grade is either 00 or 000 which is why I sometimes still use 0000 steel wool when I need ultra fine. I just make damned sure to clean off ALL the little steel fibers with oil so rust does not reappear. So far in my 45 years of Smithin' I have been successful. I will use bronze and or copper when an ultra fine grade is not so important.
I would not use any sandpaper or sanding pads as you have asked about as they will remove way more than the rust - they will remove the finish also. I start off using a 100% cotton twill shotgun patch (the least aggressive) with gun oil. Many times that in itself removes rust if it is just minor freckling or surface rust. If I need to be a bit more aggressive I move up the ladder, but I don't start with anymore than I think I might need.
BTW in all my years (50+) removing rust on metal with 0000 steel wool & oil, I have never had any residual rusting from the steel wool remnants. I understand the naysayers warnings about using steel, however as long as you carefully and thoroughly remove all the little left over "hairs of steel" no rust will return. That has been my experience. I WISH bronze wool came in a finer grade - I'd just use that, but unfortunately it does not - at least from what I have seen sold in stores and online.