Why would the uneven shape at the bottom make your measurements wrong?
The simplest way to do this is just to put some kind of liquid in the bottle (preferably a liquid that doesn't freeze in winter temperatures such as methyl alcohol). Use a commercially made thermometer to calibrate your homemade thermometer.
If you need to create your temperature scale ahead of time, based on the expected expansion of whatever's in the bottle, the irregular surface on the bottom still isn't a problem. You can fill the bottle and empty it into a beaker or measuring cup to find the volume. Measure the liquid you intend to put in the bottle in a beaker or measuring cup before you put it into the bottle. (Or just fill the bottle completely, since you've already measured the volume).
What materials are you using? There's a cheap version of this experiment, which it sounds like you're using. There's also a more sophisticated version using a test tube, stopper, and glass tubing.