It has been speculated that bubble formation of several base pairs due to thermal fluctuations is indicatory for biologically active sites. Recent evidence, based on experiments and molecular dynamics simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom, which makes an accurate calculation difficult even for minimal models. In this Letter, we introduce a new method that is orders of magnitude faster than molecular dynamics. Using this method, we show that the present evidence is unsubstantiated.