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Solving an ill-conditioned linear system with a two level preconditioned Conjugate Gradient method on the GPU presents many options. The viability of these options is studied for different bubbly flow problems. On the basis of experiments conducted, we propose strategies that make our approach computationally suitable. We use the Truncated Neumann series based preconditioning scheme in combination with Deflation for implementing the two-level preconditioned Conjugate Gradient method and test different configurations on a unit cube with varying number of bubbles. Our results exhibit up to an order of magnitude speedup on the GPU. Our preconditioning scheme combined with deflation proves competitive (in terms of computation time and convergence) when compared to deflation with Incomplete Cholesky preconditioning.