I have plans of letting go with my girlfriend when she is on her period
Is there some reason behind it?
Just the bleeding, it makes me feel bad about myself, I feel like s***.
You are not the cause of her monthly bleeding so you do not have to feel bad about it.  It is not your fault and it happens to very woman.
It's time for us to break up for my career and life then.
If your relationship is rocky, there's no need to make up strange break up excuses like blaming it on her period. How would she feel if you pointed that out, something she can't control each month? Perhaps be honest about why you want to break up so she won't have to feel ashamed about her body.