This is a good question, and one I did not know the answer to so I turned to the web.

Apparently, the burps are caused by "toxic" compounds found in the flesh of cucumbers. These compounds, known as cucurbitacins, are what cause the bitter taste as well. "Burpless" cucumbers have been cultivated to have less cucurbitacins. The amount of cucurbitacins in cucumbers can increase during growth as a result of water or heat stress.