My girlfriend recently(ish - 2 months ago) broke up with me, and I realise now that if you play yourself down, as I often did, others will either also think less of you, or will think you're just trying to get attention through it. I now realise that I think I was just after attention when I played myself down, I'm one of the irritatingly-modest people you get, and I think you are too.
To have low self-esteem when you are in a relationship with this girl, and assuming you find her very attractive, is to insult her, that she has bad taste. And those of us with genuinely modest traits cannot see what is attractive about us; I for one like to think of myself as moderately attractive (looks wouldn't stop a girl, but I would never get used for sex), mildly talented and a generally not very interesting person.
My ex-girlfriend (who(m?) I am still good friends with) retains that I have amazing eyes, am vastly intelligent (for a 17-year old) and exceedingly musically and dramatically talented. I see none of these things, but I wish now that I had just accepted it earlier in our relationship, as a partner with low self-esteem can be very tiresome (she doesn't see her attractive qualities either, though I very much can).
Luckily, I possess the talent to be fed up with myself enough that I can change things about me overnight essentially.
The bet is a terrible idea, and you should tell her that the strength of her faith in you being able to get another girl is enough to make you feel good about yourself, and call the bet off.