Aside from what WMJ said, my best advice is to memorize the tracks. One way to do it is going to time attack and getting a good time (if you unlock a staff ghost, that definitely means you got a decent time). Once you learn them, go to Grand Prix and try until you beat the cup on first place.
Seriously, that's pretty much the easiest way to do it. You will realize that the CPU on expert is actually terrible after you practice enough. Master, on the other hand...
By the way, I cleared expert with the Space Angler using jumper settings (85% max speed). Note that each car show little difference from the others with Jumper settings (only exceptions might be Blood Hawk and Night Thunder), so you will be more than okay with the Blue Falcon.
I also killed my rivals like 2 or 3 times each cup, if that helps.
Good luck!