Are you flipping the strips when sewing them together - in other words, when sewing 2 strips together. first ends out of the machine are the first to go back in for the next strip. I did a bargello years ago with mom. I started doing that; not a single bow. I tried to explain it to my mom but she ignored me; all went in the same way and it was really quite bowed. She was stubborn and I guess since she'd been sewing long than me, 'mom' knew best.
But the flipping end to end as you sew does help eliminate a LOT of that bowing. Hope this helps.