yes, exactly, "she goes to school by bus" is a million times more natural sounding than she "goes to A school by bus" which you are very unlikely to ever hear. Just possibly "the school" when a particular school is meant but "a school" is just very unlikely.
Yes, sorry, please report, still same bugs/mistakes/overlooks here... Whenever* "a" works, "the" should automatically work as well.
- OK maybe some exceptions, but you got it
"She takes the bus to school" should be accepted as well. "By bus" sounds awkward.