One good Bizarro could be Bizarro-Sinestro. Like Yellow Lantern (Bizarro-Hal Jordan), Bizarro-Sinestro would be a reluctant member of the Green Lantern Corps. He'd be Green Lantern of Space-Sector...whatever galaxy Bizarros live in.

Other bizzaros already exist.

http://www.comicvine.com/bizarro-jla/65-47966/

I know there is...but there's not a Bizarro for every DC character. Batman, Green Arrow, Lois Lane etc. are all characters that have Bizarro duplicates. But characters like the Teen Titans, Darkseid and Two-Face don't have Bizarros.

One interesting Bizarro could be Bizarro-Deathstroke. He could be a Bizarro Army soldier who had an experiment that only gave him 0.9% brain capacity instead of 90%. He is an assassin who instead of killing people for money, he tells people he's going to kill them and then poorly attempt to kill them with crap weaponry but will always fail. This would make his target very happy (Bizarro's think opposite to humans). He then pays his boss money instead of accepting it. Bizarro-Deathstroke would be a hero...well to normal people he would. To Bizarros he'd be a villain.