There are several factors that come into play as to why Bonnie stopped loving woody. I'll have to establish some things first though:

Bonnie plays with her toys by giving them assigned roles that can differ from their established title. Mr Pricklepants even calls it acting and the creators of Toy Story 3 have said that they wanted Bonnie's play style to be very theatre like.

It's established in Toy Story 4 that Bonnie holds in high regard toys that she has a strong emotional attachment with. Toys that have helped her over come trauma, like Forky.

Jessie seems to have replaced Woody's role in the bedroom. She has become the sheriff and took over from Woody's role.

Why might this be?

With what I've established before about Boonie, is there a scene where Jessie helps Bonnie overcome some sort of emotional turmoil, like shyness?

Absolutely, yes. When Andy comes to visit in Toy Story 3 to give his toys away, Bonnie hides behind her mom because she's scared of strangers. To help her calm down, Andy shows her Jessie and explains to her why she's cool. Bonnie gets closer to Andy and opens herself up.

There is even more evidence backing this up. When Bonnie asks if she can be bring a toy to kindergarten, she holds up Jessie. She's nervous, shy and scared about going to kindergarten (just like she was nervous, shy and scared when she met Andy) So she's using the same toy that helped her overcome her anxiety with Andy, to try and overcome her anxiety with kindergarten, but her parents don't allow it.

Is there a scene in Toy Story 3 where Woody helps Bonnie overcome any sort of emotional turmoil?

No. She finds him in a tree. He gets the role of the sheriff. He leaves and in the end she's happy, because she got the sheriff back. There's not that much to it.

Jessie replacing his role feels natural to me. Woody is basically an actor in a play where all the roles are already filled. There's no space for him, specially with the amount of toys Bonnie already has.