I find the Bruce and Natasha dynamic especially awesome, given his backstory.
You’re right about Natasha and manipulation etc. She can do it by force too, but mostly, she uses her image and gender as her greatest weapons to confuse, pacify, and manipulate mostly men. Women too, yes, but men are more prone to underestimate her because she’s dinky-small and pretty.
However, Bruce’s backstory comes from a place of betrayal (in MCU-verse at least). People he trusted double-crossed him. I can’t remember the exact details, but I think he was lied to about the gamma-ray experiments, so he tested it on himself because he wasn’t aware of the risks. He became the Hulk because people deceived him. He ended up on the run and hunted across the globe by them, attacked when he thought he was safe, tormented, and driven away from the people he cared about so they wouldn’t get hurt.
And the first thing Natasha does - in his view - is deceive him by sending the small child to lure him in. She may be doing it with the best intentions, trying to keep him calm and passive, but Bruce has been played before and he doesn’t like it.
Look at how she’s dressed in the first scene with him: shawl and skirt and feminine. She says she’s unarmed and without backup. She’s all sweet and gentle smiles. She’s passive and calming and gentle. But she’s also the person who not only showed up in the place he thought he was isolated and safe, but she tricked him into meeting her.
Given Bruce’s quite understandable paranoia, this is not a man who will take kindly to manipulation. She’s tricked him once with the girl, and he knows that was a stupid, amateur mistake to fall for it. He’s already suspicious anyway. So she looked harmless? So what? There are people who said they’d help him who looked harmless. You can’t manipulate a man who already anticipates the worst about you.
As for Natasha being psyched out, it isn’t Bruce that scares her. It’s what Bruce can become. She manipulates peoples’ perceptions and emotions. She plays people. But how do you manipulate something that is - for want of a better description - “a giant green rage monster”?
Natasha is all about the control: self-control and exerting some level of control over the behaviour of others to do what needs to be done. The Hulk is about as far from that as is humanly possible. She’s afraid of the Hulk because it’s something that she has never experienced before, something that can’t be played, and something that is completely out of control, and when it comes down to it, if she had to resort to physical violence, can’t be stopped.
Looking at it that way, the Hulk is quite literally Natasha’s polar-opposite: masculine, violent, primitively aggressive, senseless, and brutal. He is everything that she is not, and the extremes of those differences, the fact she knows she can’t do a thing to stop him if he decides to kill her, is why she fears him. Natasha is never one to back down from a fight, but when it comes to the Hulk, she runs for her life, because she knows there’s nothing she can do - with wits or violence - that can stop him.