Rulings

Bureau Headmaster’s last ability reduces only the amount of generic mana in equip abilities. For example, it will reduce an equip cost of {1} to {0}, but it will have no effect on an equip cost of {G}.
Some Equipment creature cards in other sets have reconfigure, a different ability that attaches them to a creature. Reconfigure is not an equip ability, and reconfigure costs are not reduced by Bureau Headmaster’s last ability. Equip variants or equip abilities with restrictions, like the “equip legendary creature” ability of Brotherhood Regalia, are still equip abilities, and their costs will be reduced by Bureau Headmaster’s last ability.