The river could symbolize a couple of things that are closely related. I think the river is symbolic of rebirth and/or freedom.
The Motorcycle Boy uses the term "Rumble Fish" to describe the Siamese fighting fish that he likes from Mr. Dobson's pet store. The Siamese fighting fish have to be kept apart from each other because otherwise they would fight to the death.
They try to kill each other. If you leaned a mirror against the bowl they'd kill themselves trying to fight their own reflection.
The Motorcycle Boy sees similarities between the fish and the gang members that Rusty-James associates himself with. The Motorcycle Boy has tried to distance himself from the gangs and violence. The Motorcycle Boy is also curious if the Siamese fighting fish would act that way in the river.
"Wonder if they'd act that way in the river," the Motorcycle Boy went on.
He eventually steals the fish from the pet store in order to release them into the river. His hope is that their newfound environment and freedom will cause them to change their ways. They are free from captivity by being in the river, so it makes sense that the river is symbolic of freedom. If the new environment does cause them to change their ways, then the fish will have essentially been reborn with a new outlook on life. This is what happened to the Motorcycle Boy when he spent time away from the gang violence in Tulsa.