Tell your girlfriend everything so that she can find a new roommate.

If she still wants to be with you and you still want to be with her then start communicating with her about that. Figure out what she needs from you to regain trust and if those things are things you can reasonably do. Learn to hold yourself accountable for your actions. Figure out if the relationship is even salvageable given what you've described above.

If she doesn't want to be with you then give her whatever level of space she needs to get over you and your betrayal.

If you don't want to be with her you need to be honest and transparent about that with her regardless of whether or not she wants to forgive you, stay together, etc. if you love someone else and aren't capable of communicating with your girlfriend around this and setting appropriate boundaries than you need to leave. She deserves to be with someone who not only loves her but who treats her well.

If things do end, regardless of whose choice it is to end it, wait to date her roommate until at least after the roommate has moved out. If the roommate and/or you share a friend group with your girlfriend then you and the roommate need to be the ones to step back from that friend group. Be prepared to both look like assholes in the eyes of some people you know and to be treated like you're assholes by some of the people you know, because you've done a somewhat shitty thing to someone you purported to love or, in the roommates case lived with, behind her back. Strongly question whether a relationship founded on this type of betrayal can actually last and whether you really want to be dating someone who would a) date their roommates ex in these circumstances of b) chose the date the kind of person (I.e. You) who would do this to their girlfriend. If you are saying you still love your girlfriend please be realistic about whether jumping into a relationship with her room ate as a rebound is even healthy.

Regardless, step one is to get off of reddit and talk to your girlfriend, own up to your mistakes, be entirely honest, respect her rights and agency in all of this and ultimately hold yourself accountable so that you treat her or anyone else you may date in the future better than you're acting here.