I agree with the others. However, in your example, you are not actually betting money. "I bet" is a figure of speech. (Admittedly, there are some men who would actually bet money on whether they could get a woman to go out with them, but most women wouldn't appreciate that. It's a crude thing to do.)
"I will bet" sounds a bit awkward unless you are referring to actual betting situations, e.g., horse races, card games, football teams, etc. "I will bet you $10 that I can do 100 push-ups without stopping." "I will bet on the next horse race" (as in "I plan to" place a bet...).
You can also use the present tense, "I bet" for actual betting situations. "I bet you $10 that I can do 100 push-ups without stopping."
In any event, #1 sounds more natural than #2.