Bischoff kind of lucked into his role as VP at WCW. He had been an announcer for WCW and did some booking for dying AWA and got the promotion because he was young, good looking, and had a yuppie attitude that was more what Turner was looking for instead of businessmen and wrestling people. Before the NWO, his biggest moves were getting Hogan and friends into WCW and starting Nitro. He was never really the head writer in the sense that Vince has never been the head writer for WWE. Kevin Sullivan was really the main booker/writer during the peak NWO stuff.
NWO idea was stolen from an angle going on in New Japan Pro Wrestling (which had a working relationship with WCW). He was removed in 1999 because ratings were tanking, buy rates were dropping, and he couldn't come up with anything new besides "Let's reform the NWO" and "Let's bring back Hulkamania". So they brought Russo in, since Russo was the head writer during WWE's biggest period, only they didn't have anyone like Vince McMahon to keep him in check. So they got rid of him in 3 months, then brought Bischoff back, then brought Russo back and their big plan was to...form a giant heel group that is trying to take over the company.