Map routes as they are driven, not as they were planned
Start by recording the routes actually driven, with stops and times, for one week. The plan and the road diverge quickly, and parents judge the service by the second version.
One record per vehicle, driver and student
Each bus needs its plate, capacity, driver and authorised substitute. Each student needs their stop and the person allowed to collect them. These are safety records, not administration.
Boarding and drop-off lists per trip
The morning and afternoon lists should be generated for the trip, checked at the gate and kept. If a child is not on the list, the bus should not leave.
Handle the exceptions deliberately
A different adult collecting a child, a student who takes the bus only on some days, a route diverted by roadworks: every exception needs a rule and a record, otherwise it is handled by phone calls that leave no trace.
Give the office the same picture
The transport manager, the front office and the gate should see the same live list. When each holds a different version, the gaps are exactly where children get lost.