As Peckish and others have said -
We have better results when we ONLY fold our bindings in half - we do NOT press them in half - that pressed line is NOT helpful when it comes to the turns - because the pressed in fold line is not where the fabric wants to go naturally.
The outer layer of the binding has to go a longer distance than the inner layer of the binding. Every time the binding is turned, the "fold line" is moved over a little bit.
I also baste the raw edges of my bindings together before applying them. It eliminates shifting of the binding edges - especially when using bias binding -so it turns over smoothly.