Handling the map in centered-player games

How can I make a huge, non-tiled map move (efficiently) around the player? I’m not sure yet, but it might include rotation.

The only way I can think of is chopping the bitmap into screen-sized chunks and hiding the parts that are not “touching” the stage, but my bitmap-related knowledge is small.

Also, how big it would be considered too big for simply moving it around without performance concerns?