Bowser's Castle course doesn't have any unique shortcuts, so please enjoy a drive-through video of the track and some advanced techniques to try.
Advanced Techniques
Power Slide
This move is especially helpful for lightweight racers because it helps them avoid losing speed through the turns. Press and hold R as you go into a turn, then use the joystick to maneuver back and forth. If you let go when the letters behind the kart turn orange, you will receive a power boost.
Power Pass
When you are gaining on another player and need a small boost to get past them, get very close to them and stay there for awhile until a small puff of smoke comes from your engine. Use the boost to leave them in the dust!
Mario Kart 64 Shortcut Video Walkthrough Series for Nintendo 64