Natasha can absolutely be bribed with her favorite foods: strawberries, Turkish Delight and Stroganoff. It’s not something she’ll ever admit of course and has to be figured out/discovered, and she’ll of course be stubborn about it, but she will eventually give in. She can also of course be bribed with vodka, but it better be the good stuff, as in the label better have Russian Cyrillic on it that you can’t understand, but she can and look like it’s older than old, though it doesn’t always quite work as well as the other three.
She cannot be bribed with material things, she’s never been materialistic, sure she likes pretty things aka lingerie, but it’s not a sufficient bribery tool given she can acquire it easily herself.
Trying to cut her off from sex won’t work either, and it will end up backfiring on you, she’ll freeze you out for longer than you’ll be able to stand it and she’ll tease unmercifully the entire time. She’s not usually one for self stimulation that much, but she does make exceptions.
The reason food works the best is the fact she cannot cook, especially not these things and yes strawberries and Turkish Delight can be bought, but it’s an unexpected thing for someone to dangle either in front of her to get something out of her or get their way. Also, home made Turkish Delight? Between that and if you make a mean Stroganoff, she will marry you and would bare your children if she could.
(This headcanon applies to not just the MCU, but Star Wars and Final Fantasy VII verses as well with the equivalent foods of those universes.)