How do you make a bow that shoots fireworks instead of arrows?

I think I have it. The operation requires four commands, not counting the fill clock. The arrow will still exist but will spawn fireworks that explode immediately.

Type this in chat:

/scoreboard objectives add ground dummy ground

1st Command Block on fill clock:

/scoreboard players set @e[type=Arrow] ground 0 {inGround:0b}

2nd Command Block on fill clock:

/scoreboard players set @e[type=Arrow] ground 1 {inGround:1b}

3rd Command Block on fill clock:

/execute @e[type=Arrow,score_ground=0] ~ ~ ~ summon FireworksRocketEntity ~ ~ ~ {LifeTime:-1,FireworksItem:{id:401,Count:1,tag:{Fireworks:{Explosions:[{Type:0,Flicker:0,Trail:0,Colors:[0],FadeColors:[0]}]}}}}

You can make your own firework to put in the execute command at http://www.minecraftupdates.com/fireworks but make sure the lifetime is set to -1.

I hope this helped and that this was what you were looking for.