Yes, I believe it is a shorter form of a phrase like 'you bet your sweet /butt/ it is'. In other words, you could safely wager a large sum on the statement being correct.
Or, remember that it means 'Of course...'
It's not exactly the same, but both are emphatic statements of agreement. Sometimes, You can say that again is said after negative comments, to emphasize that a person's feelings are even stronger than they have stated. You bet it is tends to be used for affirmative agreement.
A: Wow, that was the hardest test I've ever taken. I think I'm going to fail the class, now.
B: You can say that again.
A: I've heard that a math tutor is really expensive. Is it worth it?
B: You bet it is! I thought I would fail the class, but my tutor helped me bring my grade up to an A.