A method and system for compressing bitmap data in a system for sharing an application running on a host computer with a remote computer, wherein the shared application's screen output is simultaneously displayed on both computers. Simultaneous display of screen output is achieved by efficiently transmitting display data between the host computer and the remote computer. When a font used by the host computer for displaying text is not available on the remote computer, the host computer sends a bitmap representation of the text for display, rather than the text itself. Bitmap representations are cached by the remote computer, so that the same bitmap representation need not be repeatedly transmitted from the host computer to the remote computer. Bitmap representations are compressed by the host computer prior to transmission, transmitted, then decompressed by the computer.