I've heard rumors of a new supercarrier, something bigger than the Nimitz class has anyone else heard of this?

yeah. the george bush is a nimitz class though. it is the last nimitz. the navy is in the process of developing the cvn 21 class. their plan is to have the more modern nimitzs work with the cvn 21 to make a more powerful fleet. the geroge bush is made so that future developments made for the cvn 21 will be put on it too.

does anyone know the advantages and improvements of the cvn 21?

magnetic catapults that cause less stress to the aircraft when launching. better recovery equipment. better placement of systems like water piping and stuff like that. better defensive technologies. better computers and networking.