This is very good question, and an interesting idea for a science project. What makes this problem a little difficult is that the molecule (BPA) which you are trying to detect is present if VERY small quantities. Although these levels are not difficult to detect in the laboratory with sophisticated equipment, they may be difficult to measure at school. In the laboratory one would use a machine called a UV-vis spectrometer to determine if the BPA were present. However, there may be another way to say qualitatively whether BPA is present in your water bottles after heating. What I would suggest is that since the BPA molecule has two alcohol groups attached to the phenol rings it has some acidity to it. This acidity value is reported as pKa=9.73 (calculated using Advanced Chemistry Development (ACD/Labs) Software V8.14 for Solaris in SciFinder Scholar 2006.

You should look on Wikipedia to see exactly what pKa means, but it is kind of like pH. For comparison pure water is pKa = 15.74, so you can see that the BPA is more acidic. This being said, you may be able to do some simple pH measurements in order to determine if BPA is present in your water. If the water is more acidic after being put into the plastic bottle and heated then this is a possible indicator that BPA is being released by the plastic. If you do not measure a change in a large volume of water then you may try heating the water and then waiting for a lot of the water to evaporate before trying to measure the pH, this may concentrate the solution and improve the possibility of success of your measurement.