During the trek from the prison - Natasha had opted not to use a vehicle to prevent any undue attention to them - the Russian had been fairly quiet, focusing on her senses as they walked, rather than her companions. Despite that, she was innately aware of every move Clint made - whether it was walking at his normal gait or any time he favored his injured ribs. She hadn't been entirely certain that him leaving was a good idea, but when it came down to it, Natasha trusted Clint and knew he'd suffered worse than bruised ribs in their past missions together. And she knew that he wouldn't be there if he seriously thought he might hold them up or be a weak point. Having him there in general made Natasha feel better, too, trusting him completely to watch her back and thus keep her from having to concentrate on a three hundred and sixty degree radius. It was easier, in the long run, to have him with her.
Julia was the one that Natasha wasn't entirely sure of, but she was glad that the nurse had insisted on coming. While she would have gotten Bruce to meet them anyway, having someone with them from the prison would not only give Natasha a chance to gauge her, but it would build trust between them, and help, in the long run, with her cover. Honestly, Natasha knew how to dress wounds, field first aid and the like, but she wasn't a doctor...far from it, in fact, and neither was Clint. If Connor was sicker than he claimed, neither would have been able to tell and they might have ended up bringing some sickness back to the prison itself, endangering everyone.
As they neared the burnt out church, she raised a hand to stop the other two, and nodded to Clint to cover her as she moved forward, one hand resting on the butt of a gun worn in a hip holster, jade eyes searching for some sign of the man they were to meet.