This is the easiest way to remove the rusted toilet tank bolt.
Tools:
A small vise grip plier.
A socket that fits the nut.
Use the plier to grip the end of the bolt inside the tank. It has the most grip when the plier is horizontal to the tank. While the plier is bracing against the wall the tank your hands are free to work on the nut at the bottom. Use the socket to turn the nut at bottom. Even better if the bolt break while you turn the nut.