Bearings-only localization is a problem with applications in the communications and defense sectors. Although the problem of point estimation for bearings-only localization has been well explored in the literature, there still exists a significant need for methods for interval estimation, particularly methods which are non-parametric in nature. This thesis applies a non-parametric statistical technique called the empirical bootstrap to accomplish two goals. The first is the application of the bootstrap to develop a novel, non-iterative, asymptotically unbiased estimator for bearings-only localization. The second is a method which leverages the bootstrap, as well as the aforementioned estimator, to estimate two-dimensional confidence ellipses for bearings-only localization. The development of these techniques is supported by simulation study over a range of scenario geometries and noise models, and the results are shown to be competitive to current techniques, if not preferable, depending on the particular problem domain and situation.