Subject to certain exemptions, under Regulation 9(2) of the European Communities (Compulsory Use of Safety Belts and Child Restraint Systems in Motor Vehicles) Regulations 2006 - S.I. No. 240 of 2006, every adult and every child of 3 years of age or more occupying a seat in a category M2 or M3 vehicle, which includes school buses, is required to wear a safety belt or an appropriate child restraint system. A person (other than a person under 14 years of age) who fails to comply with this Regulation commits an offence.
Regulation 9(4) provides that the driver of a large public service vehicle is not obliged to carry a passenger who, without showing reasonable just cause, fails to comply with the aforementioned Regulation, while under Regulation 10(2) the owner of such a vehicle shall ensure that passengers are informed of the requirement to wear safety belts while they are seated and while the bus is in motion.
As with all Road Traffic legislation, enforcement of these Regulatory requirements is a matter for An Garda Síochána.