The bias-variance tradeoff is the idea that learning methods need to balance model complexity with data size to minimize both under-fitting and over-fitting. Recent empirical work and theoretical analyses with over-parameterized neural networks challenge the classic bias-variance trade-off notion suggesting that no such trade-off holds: as the width of the network grows, bias monotonically decreases while variance initially increases followed by a decrease. In this work, we first provide a variance decomposition-based justification criteria to examine whether large pretrained neural models in a fine-tuning setting are generalizable enough to have low bias and variance. We then perform theoretical and empirical analysis using ensemble methods explicitly designed to decrease variance due to optimization. This results in essentially a two-stage fine-tuning algorithm that first ratchets down bias and variance iteratively, and then uses a selected fixed-bias model to further reduce variance due to optimization by ensembling. We also analyze the nature of variance change with the ensemble size in low- and high-resource classes. Empirical results show that this two-stage method obtains strong results on SuperGLUE tasks and clinical information extraction tasks. Code and settings are available: https://github.com/christa60/bias-var-fine-tuning-plms.git.