There are two definitions of this term, but in context the main definition (see link below) is wrong because the Royal Academy is not a government authority. Usually in the UK, "bye-laws" are local laws passed by local authorities. They are valid only in the jurisdiction of that authority. In that context, the term is best translated as "ordonnance locale" (or plural equivalent).

In this case, we're talking about the internal rules of an educational establishment. Hence, reglement (with "accent grave" over the first E) administratif, or plural equivalent.