I'm going to ask for a rent reduction because my roommate's girlfriend is here all the time
What are the chances that this will be successful?
Around 50% with the evidence I found about her
Your roommate's girlfriend is not your girlfriend and if she is there all the time and making things inconvenient for you, you are right to negotiate. You did not initially agree to have an additional roommate in this living arrangement so it makes sense to re-negotiate in this case.
Exactly. Her being here all the time makes living here uncomfortable with me.
If that's the case, then talk to you roommate and re-negotiate terms. Given the situation as you describe it from your perspective, a rent reduction is warranted.