Murdoch, who was appointed to the board in March, purchased 150,000 ordinary shares on June 5 for total value of $20,050, share marking her first purchase in the company.
The company's shares last traded at 13 cents.
Murdoch has more than 28 years of experience in the resources and infrastructure sectors in Australia and internationally.
With an honours degree in law, her mining sector experience includes senior operational roles with AMCI investments, MIM Holdings and Xstrata Queensland.
Last month the company’s chairman Stephen Everett and managing director and CEO Simon Finnis addressed shareholders on its successful transition from developer to operator.
It noted bauxite production in 2018 went as planned, laying a proof-of-operational concept given production guidance was met even with external challenges such as weather.
Addressing the AGM, Everett said: “I think it is fair to say Metro is on its way.
“We shipped over 2 million tonnes of bauxite in 2018 and we have announced upgrade production guidance to 3.5 million tonnes for this year.”