If you ask someone to bring their own code, you are assuming they have some code to share that they are also confident enough in to bring. I can see lots of people agonizing over this. Even if you've got a relatively broad base of shareable code you've written, what's right for the context of the interview? It would be stressful for a lot of people, probably more than just doing a coding exercise.
I'd suggest giving people another option as well.