When I was first starting out, I took on a Ricky Timms Harmonic Convergence pattern because I thought, "It's all straight lines, how hard can that be?"
Well, I sewed one strip to another and ended up with a terrible bowing. You'd think I would have noticed that even though I was starting with the pieces lined up together, I wasn't ending with them together -- one piece was a little shorter each time. (Actually, I did notice, but I disregarded it, because as I said, I was just starting out and I was a little careless that way).
Anyway, I ended up with a big piece of fabric with a gentle curve throughout. I was crushed. I ended up cutting it into a big fish shape, because that was the only shape I could fit into the weird shape I had. I thought I'd either make a big fish pillow or stitch it down onto a piece of fleece. In truth, I hid it away because it was such a disaster.
I saw it not too long ago...maybe I'll try to fix it. Nah. But don't feel bad about your bowing, just sew in alternate directions, like the others have said!