When I piece the binding, I use diagonal seams and press them open so the finding folds nice and flat.
Instead of a bias tape maker, I put a long pin in my ironing pad - in, tin space then up and then in again about 1 1/2" over. I fold the tip of the fabric in half and pull it through the long space of the pin, ironing as I go. It is (for me) faster than the bias tape maker and I can press the whole strip.