The rule of thumb I seem to remember is to add a half-size for bands 5mm or wider -- so if you usually wear a 9.25 for a 2mm band, you would wear a 9.75 for a 6mm band.
I think this general guideline refers to same-fit shanks, so if the 2mm band is a comfort-fit band, and the 6mm band will NOT be -- or vice versa -- if the 2mm band is NOT a comfort-fit and the 6mm band WILL be -- then you'd need to take that into account and adjust upwards or downwards as appropriate.