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The problem of bias, meaning over- or underestimation, of the component perpendicular to the line-of-sight, Bperp, in vector magnetic field maps is discussed. Previous works on this topic have illustrated that the problem exists; here we perform novel investigations to quantify the bias, fully understand its source(s), and provide mitigation strategies. First, we develop quantitative metrics to measure the Bperp bias and quantify the effect in both local (physical) and native image-plane components. Second we test and evaluate different inversion options and data sources, to systematically characterize the impacts of choices, including explicitly accounting for the magnetic fill fraction ff. Third we deploy a simple model to test how noise and different models of the bias may manifest. From these three investigations we find that while the bias is dominantly present in under-resolved structures, it is also present in strong-field pixel-filling structures. Noise in the magnetograms can exacerbate the problem, but it is not the primary cause. We show that fitting ff explicitly provides significant mitigation, but that other considerations such as choice of chi^2 weights and optimization algorithms can impact the results as well. Finally, we demonstrate a straightforward "quick fix" that can be applied post-facto but prior to solving the 180deg ambiguity in Bperp, and which may be useful when global-scale structures are, e.g., used for model boundary input. The conclusions of this work support the deployment of inversion codes that explicitly fit ff or, as with the new SyntHIA neural-net, that are trained on data that did so.