The bowing might be caused by uneven feed of top and bottom fabric. I had sewn a lot of long 1" strips and most of them bowed. At one point in the middle of the process I got a new machine with an integrated walking foot and the LQS recommended using it for piecing. The bowing stopped.
Try using a walking foot to sew your strips. If you don't have one - try playing with the presser foot tension to get an even feed of top and bottom fabric.
It could also be a tension issue, sometimes the tension is off just enough to bow the fabric, but not enough to show a bad stitch.
A lot of starch helps as well.