Measuring free energy differences between states is of fundamental importance to understanding and predicting the behaviour of thermodynamic systems. The Jarzynski equality provides a method for measuring free energy differences using non-equilibrium work paths and represents a major advance of modern thermodynamics. Recent work has extended the theory by using work paths in both directions between the states to improve the accuracy of the free energy measurement. It has also been shown that the Jarzynski equality can be adapted to measure the free energy of quasi-equilibrium systems such as glasses. Here we combine these advances to accurately measure the free energy difference between a glassy state and equilibrium using bi-directional methods. For this system however, the result is not as accurate as that achieved using the work evaluated in a single direction.