I imagine the words once and twice do not have their usual modern meanings here. The word twice must mean �second time�, and once means �first time�. Like skipping and counting the jumps, once, twice�.
Therefore the meaning is: If bitten the first time one tries something, then the second time, one will be shy. A more concise modern translation of the phrase would be first time bitten, second time shy. But that is too garbled and lengthy for idioms.
The following: Once bitten, two times shy is almost certainly not the correct meaning. The saying could be generalised to:Once bitten, twice bitten, thrice shy.
This means that if you are bitten the first two times, you will be shy the third time. This could be shortened to:
Twice bitten, thrice shy.