Exhibition Rush is a mode where you are rewarded points for earning different boosts and hitting opponents with weapons, you get a higher point multiplier the higher you are placed in the race.
There are various ways you can get this but one of the easiest it to have a weapon saved up like Ricochet Bubble (So you can fire behind you) and while in first earn a KER from the blue areas of the road as in 1st the KER will earn you 800 points and hitting the opponent will take you over the 1000.
To setup up an Exhibition Rush event press 'Play - Go!' and press
to enter the custom settings and change the game mode from there.