To many statistical questions you can get frequentist and Bayesian answers which actually coincide. Such a subject is covariance matrix shrinkage and Bayesian regression.
Have a look at the article "Honey, I Shrunk the Sample Covariance Matrix" from Lediot and Wolf. They introduce a transformation of the covariance matrix, so that the diagonals become more pronounced, hence less (over) fitting happens on the correlation matrix when doing regression.
Similar -- shrinked -- covariance matrix can be used in regression and you will arrive to ridge regression (L2 regularization) or Lasso, LARS (L1 regularization). These regression methods are expressed as minimization of the quadratic error term plus an L1 or L2 penalty term on regression weights. Consider L2 regularization for example, which minimizes:
$$\|A\mathbf{x}-\mathbf{b}\|^2+ \lambda\| \mathbf{x}\|^2$$
While at first this looks like frequentist formula aimed at reducing over-fitting, is is equivalent to the Bayesian solutions of regression with Normal prior on the regression weights (the penalty coefficient $\lambda$ is a function of variance of the Normal prior).
Many statistical packages are equipped with L1 and L2 regressions and covariance shrinkage (e.g. scikit-learn in Python), so you won't have to get your hands very dirty.
An other interesting Bayesian model in portfolio optimizaiton is the Black-Litterman model, where they use a reasonable prior on expected asset returns (derived from reverse optimization in portfolio theory), and Bayesian theory to arrive to a mixed estimation of future asset returns.