Yesterday I bought Pokemon Yellow, and have been playing it for hours on end. Then today, I got the new Pokemon 20th Anniversary 3DS as a gift. I want to dedicate the new SD card to Pokemon, but I was wondering if I could transfer only the Pokemon Yellow and Pokemon Bank Data over, or would I have to bring all my other games with it?
You must transfer all or nothing. Nintendo does this to protect it's digital content from piracy and such. You must transfer your entire account. I got the new 3ds Hyrule Edition and performed the wifi transfer from my old 3ds and it was a very strict and unforgiving process. Also only one 3ds can be attached to each account per Nintendo's account help page.
You could theoretically set up a new account on your new 3ds and use that account only for Pokemon. But you would have to buy Yellow again and start the game over.