It's a real obscure word that Sheldon's actor overheard and decided it was funny to use. From an interview with AOL:

"One of the writers, he used to say it, apparently in the writers' room. That's the tale I've heard. But I remember it wasn't in a script. It was one of those moments where we'd work on a scene and then you'd go and take notes from the producers and writers. If I'm correct, it was inserted right before a taping basically. It was like 'That would work in here. What if he said 'bazinga' after that?'" He admitted the audience may not have known what it meant at first, but it caught on for a familiar reason. "The writers liked it but they knew what it meant. But I knew what it meant the moment they said it. It's like 'gotcha", you know, it's just in that energy. There's just something about it. I like it because it's not plain English in a lot of ways and that's very handy."