I need to do a small tute about tacking. I tack everywhere seams meet and on the ends where the seam will go through. This way the fabric can't stretch. Tacking is just putting a stitch or two in place so the fabric can't move.
Then as you sew the two fabrics will be fine and wont' stretch.
I've never had any problems with bias. You can also put pins in if you like along the edges to keep the fabric in place. I rarely use pins but in some cases it helps.