Look .... only in a comic book arc would you get something as silly as a brainwashed agent who's re-animated specifically for missions having time to date another agent. This kind of thing happens because those CBM writers have to keep coming up with new material.
In the MCU, the relationship that CA:TWS will spend a little time re-visiting is clearly Steve and Peggy. There's just no reason to even go the ridiculous route of establishing a BW and The Winter Soldier romance . Besides, in The Avengers she pretty much established she doesn't care about that kind of thing when she spoke with Loki.
Now, the idea of them having trained together or worked together in some capacity makes complete sense to the narrative.