What is the difference between she doesn't like bearing herself open to people and she doesn't like opening to people ?Feel free to just provide example sentences.

I think in the first sentence it would be "baring" as in to "bare one's soul, bare one's emotions" etc. to make "bare" is to expose, uncover, unclothe, etc.

to "bear" is to carry a burden or a load, so it doesn't go with opening up one's interior thoughts or emotions.

for the second example, we would say "to open up TO someone."

So if you were to say,
"She doesn't like baring her emotions/thoughts/feelings to others."

or

"she doesn't like opening up to others/ opening herself up to others."

...they basically mean the same thing.

"baring" one's emotions might connote a bit more exposure or intimacy, but the meaning is essentially the same between the two.