When cutting strips, or really almost anything, I start with tearing the fabric to find the straight grain. That way there is no question but that I'm cutting on the lengthwise grain. It helps. You'd be surprised, or perhaps appalled is a better word, at some of the truly crooked grains I've found, even in the expensive fabrics! I always get an extra 1/4 yard because I know I'm going to be tearing some off. And if I have to "even them up" after several cuts, I tear the fabric again, to find the straight grain. Some people would call this wasteful. I consider it less wasteful than ending up with a whole bunch of crooked strips I can't use. And I don't have a bowing problem with strip piecing either, I think partly because my strips are so straight. I also sew each strip from the opposite end, of course, and I'm sure that helps.
I hope you get your problem solved! Strip piecing is such a great way to make quilts!