Before every operation and assignment, there is always at least a little time to prepare. Hits at various points throughout the films.
When Natasha was assigned to go undercover at Stark Industries, she just sighed and asked for an extra day or two to go shopping and work on becoming "Natalie Rushman," personal assistant, because after reviewing the assignment she wasn't quite sure that she had the right clothes. Agent Coulson nodded, Accounting reminded her to save receipts, and Clint had started to sing "Pretty Woman" under his breath, so she decided that he had volunteered to come and hold bags, as well as help her study her cover story. She had used this persona before, but each time there were minor tweaks that she had to learn and integrate, and she really did need some new clothes.
She makes him drive to a mall, a big one near Philadelphia, while she's scanning some notes on the last time she had had to become Natalie, and on their arrival she takes Clint's arm and sweeps into the mall as he mutters "touch less rich, Nat," as he shifts her grip from his elbow to his hand. Dropping her chin slightly, she senses more than sees his nod. Clint was always good at noticing the really minute details, and how to make everything seem seamless. It still doesn't get him out of any potential embarrassment, yet, so their first stop is for lingerie. She makes him go inside, and hold the bag.
Over lunch in the food court, Natasha considers how to best keep in touch. SHIELD communicators might be a little too obvious if she kept one on her at all times, so their options are mostly limited to face-to-face meetings and coded texts, phone calls, and e-mails. It would be easiest if she just re-used previous methods, so long-distance boyfriend, family...she frowns slightly, not remembering where Natalie's family lives. Glancing across the table at Clint, who appears to be enjoying something dripping with fat and grease, she allows a slight look of disgust to come across her face. "I can't believe you like that stuff babe," she declares, picking at her salad. "I mean, look at it!" The smallest wink, barely a flick of an eyelash, when he catches her eye. A flash of humor in his says that he caught it, and understands the meaning.
"But, Nat, lookit me, I'm a growing boy! And with you taking this job all the way out in California, I'll need to fill that empty space in my life." And then he starts humming "Every breath you take," and she snorts, picks up their meals, and dumps them in the trash, ignoring his protests. They're all fake, because she knows that he really didn't like his meal all that much. She still makes him carry all the bags, but allows him to hide the pink one.
They don't return to the Helicarrier but head to a SHIELD safe house in Delaware, where they cut all the tags off the clothing and wash everything twice. She tries on various combinations, with Clint lounging on a sofa, a TV tuned to the Stark Expo in the background, as he works on making things like her makeup look just slightly used, and reprogramming her cell phone. He helps her pack it all up in suitcases they had brought along, holding back a couple outfits so that she'd be able to get to California. She also takes the time to pull up on the computer the rest of Natalie's background information, printing it out and tossing it on the table.
The rest of the time in the house is filled with the two of them re-establishing codewords and trouble phrases, which range from mild boredom to "if I don't get out of here now I will kill Tony Stark. Slowly. With a hairpin."
When Phil Coulson arrives with additional personnel, she is in full Natalie-mode, Agent Natasha Romanoff of SHIELD in a small, walled-off corner of her mind. She even hums along with Clint, because Natalie likes how her boyfriend knows all these random songs that say something, even if Natasha wants to tape his mouth shut, tie him down, and force him to watch endless amounts of Russian ballet. She even steals one of Clint's t-shirts, because that's just the way that Natalie is when she isn't working.
The next day, Natalie Rushman boards her flight to California.