I’m tempted to ask her out again...

I am a 27-year old guy and have been in love with a woman two years younger for a long time. We used to be in college together and I have known her since our first year. She knows I like her because I once told her how I felt at a party. She didn’t react, but we connected on Facebook, and I have an idea of what’s going on in her life. She recently ended a relationship with someone she was dating for three years, and I have been tempted to get in touch with her and ask her out. The reason I haven’t done this yet is because I don’t know if she has changed her mind since I first told her how I felt. She may simply be looking for a rebound relationship, which will backfire because she may dump me the minute she feels better. I really like her and don’t want this to be a temporary thing. What should I do?
There are a lot of preconceived notions you appear to have about this woman. You assume she is looking for a relationship simply because she ended one, then assume it will be a rebound, and then assume it will be with you. Why not just ask her out for a cup of coffee, chat with her as a friend, and get a sense of how things are with her life before jumping to conclusions? It’s always better to try and build a friendship if you hope for a relationship that evolves into something deeper. At the very least, you may finally get an insight into whether she has any feelings for you to begin with.

Should I end a relationship just because my girlfriend thinks we aren’t serious about this? I think I am, but she doesn’t agree with me at all.
If she doesn’t agree, it’s probably because you haven’t done much to prove what you say. Actions make a difference, and you probably need to work on better communication too.