'Betted' is an alternative to 'bet', as the past participle and simple past, and can be useful in eliminating ambiguity in phrases such as, 'We bet on it'.
I'm not surprised that you have never used 'betted' but that you have never come across it before does surprise me. It's listed in all good dictionaries and verb tables as being the regular form. It is admittedly far less common than the irregular 'bet' but I can't answer your question with any degree of certainty.
I am getting confused. If most of the people are saying that "Bet" is correct then I will go with it. Can we say "I have bet my money or car for this bet or race or matter" or "We have put on a bet on this".