Most ridges are easily eliminated by heating the bottle for 1 to 2 minutes. During the heating process the plastic gets slightly softer and the internal pressure (as the cap should remain closed) straightens and rectifies the bottle's surface, automatically eliminating ridges.
You'll be able to see this process performed on a ridged bottle by a heat gun on this video:
Please feel free to perform this test with your stove on low heat and any bottle. In a couple of minutes you will see that your bottle will be smooth and ready for cutting.