A unwrapped stack of $50's or $100 bills, amounting to either $5,000 or $10,000, like what you would see in a bank vault, with the paper label still wrapped around the center of the stack of bills. Breaking the center wrapping paper does not make the term bundle invalid, but the act of pulling one bill out and restacking it, no longer makes it a bundle, it is now considered a stack.
One bundle is usually $10,000, or 100 $100 bills.
Half a bundle is $5,000, or 100 $50 bills.
Sources: professional poker, those who roll with lots of cash on hand.
I usually keep one bundle on my person, or $10,000.