I started making Bargello quilt several years ago. I cut it all, and was sewing it at my mothers for something to do during a long vacation. I had already made a small wallhanging size before. So once I started sewing I also experienced the bowing effect. It discouraged me and it's still haunting me - it's still in a bag in my sewing boxes. Someday I'll get back to it.
Anyway, what was happening was that my mothers machine is pretty old, and the pressure wasn't even. It was pushing the top layer out farther than the bottom one. Then I was also sewing everything from the same direction which made it even worse. Try making a couple of strips that you know are exactly the same length and see if your maching is pushing one out farther.