We give a formula for connected n-point functions of a tau-function of the BKP hierarchy in terms of its BKP-affine coordinates. As examples, we show how to compute the connected n-point functions of the Witten-Kontsevich tau-function, the Brezin-Gross-Witten tau-function, and the tau-function of spin single Hurwitz numbers. These connected n-point functions are known to be important invariants in geometry. We also propose a method to find the quantum spectral curve of type B using BKP-affine coordinates. This talk is based on joint works with Ce Ji, Chenglang Yang, and Qingsheng Zhang.