I'm putting a bedroom in a basement. There's already a window above ground level. Do I need to dig down and install a special egress window or can I just put in a bigger window that meets requirements and codes?
An egress window has nothing to do with a window being below above/below grade. Egress means "go out". An egress window is a window that someone can safely exit in the event of a fire where there could be blocked paths through the rest of the house. Egress windows are typically required for all bedrooms in a modern dwelling regardless of where they are located and are typically sized to fit a firefighter fully suited up in firefighting gear.
If there is sufficient clearance to add a basement window that meets the qualifications for egress without digging according to local building code (distance from the floor is probably the biggest determining factor in your case if your basement has tall ceilings), then this would qualify as an egress window and you would not need to dig or add an associated egress window well.
Where emergency escape and rescue openings are provided they shall have a sill height of not more than 44 inches (1118 mm) measured from the finished floor to the bottom of the clear opening.
Emergency escape and rescue openings with a finished sill height below the adjacent ground elevation shall be provided with a window well in accordance with Section R310.2