This approach may require a bit of retconning of Captain America: The Winter Soldier, but seeing Black Widow in a gritty espionage movie opposite frenemy Bucky Barnes would be certainly be a different kind of Marvel movie.
However, as of right now, it is looking more likely that the Black Widow movie may see her tangoing with the Winter Soldier.
Fans have long wanted to see the Budapest mission with Black Widow and Hawkeye that was mentioned in The Avengers, and this timeframe may open up that as a possibility.
Sebastian Stan has spoken about this possibility in the past, citing the comics where the two have a more complicated relationship, as Bucky is a mentor and even lover to Natasha.