My gf has other men options. Help?

What if my girlfriend has other men options? It took me 2 years in the relationship to win her heart fully, and to even hear the words "I love you" from her. And I'm so in love with her because she has taught me a lot of things in life. The problem is not does she only treat me like her boyfriend, she treats me like her besfriend too. We were very close friends before we got together so I guess she got used to telling me everything. She told me everything about her previous sex life, love life, everything you can think of. And yesterday she told me there's this guy who asked her out about a week ago. She said she felt like a horrible girlfriend when she didn't know what to answer to the guy. I felt very hurt at that point of time considering the fact she couldnt just say no to the guy, but she has admitted her guilt. I've seen the guy on Facebook, and I must say he's quite a competitor. My girlfriend has told me that she's ashamed of herself for even wondering for an answer, and wanted me to guide her with this. So I told her to immediately stop all contact with him, and say no to him because she has a boyfriend. She said okay, but the thing is I don't know if she would really do it because a few days back she did ask me "What if a better girl came your way, what would you do?" At that point of time, I didn't know her intentions for asking but now I know. Will I lose her to him? She's quite independent and honestly speaking, she'd probably do fine without me or the other guy, but I'm just afraid of losing her, especially to other guy considering the fact he's quite a looker and has the brains. What should I do to not lose her??