Can bidding above the current price be a solution to ensure your
machines never get stolen?
Yes, this is called an auction. The highest bidder gets the machines. Most people will have a limit what they are willing to pay though, this is how the system works. In the hypothetical situation where everyone increased their bids without limits, then if machines are in short supply the price would also grow without limits.
Suppose that the current price is 1$ and my "maximum bidding price" is
2$, what will I pay?
As far as I understand, you pay the current price.
Pricing
You pay the Spot price for Spot Instances, which is set by
Amazon EC2 and adjusted gradually based on the long-term supply of and
demand for Spot Instances. If the maximum price for your request
exceeds the current Spot price, Amazon EC2 fulfills your request if
capacity is available. Your Spot Instances run until you terminate
them, capacity is no longer available, or the Spot price exceeds your
maximum price.
[EDIT]
Re-reading, I think your machines can still be terminated if your price is above the spot price, but the capacity is no longer available. I assume this is because needed capacity can change quicker than spot price.