I grew up in a suburb. I biked around just fine. We have a bus stop just down the street from where I live now. However, I would let my kids carry a gun before I would let them on a bus.
That's likely because you live in a car-centric place where buses are generally only used by poor people, causing it to inherit a stigma.
Transit in car-centric areas is generally under-funded, with low frequency service, so really only those who have far more time than money are likely to use it (see previous paragraph). Nor are the routes oriented towards parks, the beach, the local library, or other places kids would go to to meet their friends.
Taking a bus can also be confusing for a beginner. I didn't start using the bus until visiting the UK in my late twenties. I didn't know how to pay, I didn't know how to request a stop, I didn't know what I could ask of the driver, I didn't know the route or what the stop looked like, and more.
If you don't have the experience yourself, and your kid hasn't been with you on the bus to learn from you, then of course you are unlikely to want your kid to use the bus.
On the other hand, go to the UK and you'll see that kids take the regular bus to/from school, along with people doing the work commute or running errands.
There isn't a fleet of student-only school buses, because the mass transit system has enough capacity and frequency. There I am on a double-decker bus on my second day in the UK and to my surprise the bus stops near a school and a gaggle of teens (okay, maybe 15-20) climb aboard.
And the UK is pretty car-centric compared to what I've heard about the Netherlands.
