There are a lot of moments that encompass Bay and Emmett's relationship. These are the ones that Emmett remembers.
Bay/Emmett e-mails. Season 4.
Bay learns to appreciate Emmett's game nights.
Bay took the fall for Daphne, but she can't let Emmett do the same as well. He has to go to LA, and they'll either survive or they won't. One-shot. Some small season 4 spoilers.
Emmett surprises Bay with a visit. Again, slightly spoilery, based on part of the season 4 promo. Sexy times!
A painting of Bay's brings back a childhood memory for Emmett, one that includes Bay. Bay-Emmett meeting as children/fluff. Really short one-shot/drabble.
Bay has never really explored the concept of past lives or soul mates, until now that is. And what she finds is she's had a few different lives and always comes face to face with one person, Emmett. One-shot.