Actually, the idiom is "you can bet your boots" (never "I," always "you"; and never with the preposition "on"). It means you can be 100% sure. Other idioms like this are "you can bet your bottom dollar" and "you can take it to the bank." Example: "You can bet your boots that the boss will find something to criticize in this report."

Never heard of it. I think you have it wrong. Maybe: I bet my boots on that. I bet 10 dollars on that. I be my car on that. I bet my [just about anything can go here] on that.