The bonus room duct run is probably the longest run in the duct system, which means other register/diffusers will get almost all the air unless the system had balancing dampers and was properly balanced, which it obviously was not.

A fairly simple and cheap approach would be to install an in-line booster fan in the branch duct that supplies the bonus room since it sounds like you have attic access to the branch duct. You would want to install it as near as possible to the point where the branch duct takes off from the trunk line.

The biggest challenge will be the electrical connections and controls. Ideally, the booster fan would be interlocked to run anytime the furnace blower runs.

Also, while you're in the attic, do a thorough check to ensure that the ducts don't leak air, and that they are well insulated with a vapor barrier on the outer surface.