Headcanon

Bobbi is set post-Widowmaker, but before she joins up with the New Avengers.

She has a doctorate in biochemistry, specializing in neurotoxins. It’s this work that led to her being recruited by Fury in the first place.
She’s more than capable of being cold, calculating, and vicious (particularly since Hawkeye’s death) and isn’t afraid of using torture to get the information she wants.
Since being kidnapped and tortured by Vanko, then murdered and resurrected by Constantine, she’s been dealing with PTS, manifested mainly in bad dreams. Despite this, she’s not likely to seek help.
Has a mediocore track record with men; there have been a few boyfriends in the past, but no one serious. Her failed marriage with Clint speaks for itself.
For all her outer strength, Bobbi can be very insecure, even if she doesn’t let it show. There are periods when she doubts herself and her work as an agent. These usually end in her beating someone up or working herself into the ground.
She takes her training as a spy very seriously and can therefore be very cautious. She tries to avoid making snap judgments and prefers to wait on a situation until she’s collected and evaluated all of the available information.
She’s naturally quite flirty, but knows when, where, and with whom to draw a line. In the bedroom, she likes things a little kinky.
Bobbi likes flowers, just not when they’ve been cut. She thinks they’re much prettier when in a garden with other plants. Her favorite flowers are purple irises.
Secretly, she’s a bit of a girly girl. She has a huge soft spot for pretty clothes and fancy shoes, but rarely has an opportunity to wear. On the rare occasion that she does wear civilian clothes, she prefers practical clothes like jeans and sturdier tops.
She loves singing, and is actually quite good, but doesn’t like to tell people because she’s been teased about it in the past.
Bobbi enjoys baking, but is an average cook. Her mother taught her how to bake from a young age.
Though she’ll never admit it to anyone, she’s jealous of the other versions of herself. She’s jealous that they had time with their respective Clints and had actual relationships with them.
She values loyalty. If you’re a member of her team, she’ll trust you unless you give her a reason not to. If you betray her trust, be prepared to deal with the consequences.
Bobbi does yoga to keep flexible and work on strength training.
She owns a small island in Tierra del Fuego that she goes to when she needs space. There’s a small, but modern cabin, with quite a cache of weapons. No one else lives on the island, so she uses it for running solo training missions. When she does go to the island it’s usually because she doesn’t trust herself to be around other people. She takes her aggression out on the animal population and hunts for all her meals.
The only person allowed to call her Barbara is Director Fury, on pain of death.
The tapestry with Yggdrasil hanging in the front entry way? A gift from Frigga, after she was turned into a kid and sent to Asgard to be babysat for a night. She treasures it.
She has a bigger abandonment complex than she’ll admit to anyone. It stems from almost everyone close to her either leaving, dying, or betraying her. As much as she wants to let people in, she can’t seem drop her guard enough to actually let that happen.