When I do curved corners, I only do the curves with bias binding and the rest with regular binding. You have to take the time to measure and mark where you want the bias pieces to go but worth the work.
Personally, I have never had a problem doing bias binding and if you are hand finishing, the thread just disappears into the fabric. If the baby quilt will be used a lot, the bias binding is also longer wearing because of the cross grain of the binding.
Be sure to show us the completed project.
peace