Ultimately, the only person that cares about your children in the world is you. A school bus driver only cares about getting paid. The same is true for a teacher. The same is true for a person who provides social services or judges a family law case. A child is the most safe with his biological parents.
Yes, I would feel safer driving my children to school because at least my car has seat belts. Busses should be required to have seat belts from now on and it makes no sense that innocent children are sent to school without them. They have no way of protecting themselves.
On the one hand there is no telling who is driving my children. They may have a record for driving drunk or under the influence. Of course there are other risks when it comes to having strangers driving my children They may not have had the most extensive background checks and may be a rapist or pedophile. There are a lot of things that could happen to the children.
Although this is a tremendous tragedy, the reality is that this type of thing does not happen often at all. I cannot recall the last time I heard about a serious school bus crash. It's unfortunate, but it is a risk that you take, no matter what mode of transportation you take.