I do alot of narrow borders. My two biggest tips ... STARCH and a 1/4 inch foot. I use starch concentrate full strenght , and immerse the fabric in the starch , hang dry , press, then cut the strips. I would not attempt a narrow boarder with out my starch! It REALLY makes a difference.
If you can not get the concentrate , use spray , but allow it to dry , then spray again, dry, then press and cut.