Well, Marvel Movieverse has her in her 20s. Marvel comicverse has her being in her 70s (for real), a product of the Russian supersoldier program. That's how she knows Bucky/The Winter Soldier. They trained together and were lovers. Comic canon has Nat originally being one of the bad guys, and she seduced Clint to be her sidekick, when she was off hunting Tony Stark.

So.

Y'know.

You get to choose. :D The canon's pretty cracked out.