I think the "I'll bet you..." form is more standard in the US, but saying "I bet you..." is definitely acceptable, and in my experience is actually much more common in some other English-speaking countries (e.g. England itself).

That's strange. I can't find a single example online where "you" isn't the subject of the bet (for example, I bet you look good on the dance floor).

Paul Graham has managed to set himself up an army of nitpickers (free editors).

An alarming vision.

http://dictionary.reference.com/browse/nit