Bi-skew braces and regular subgroups of the holomorph

L. Childs has defined a skew brace (G,⋅,∘) to be a bi-skew brace if (G,∘,⋅) is also a skew brace, and has given applications of this concept to the equivalent theory of Hopf-Galois structures. The goal of this paper is to deal with bi-skew braces (G,⋅,∘) from the yet equivalent point of view of regular subgroups of the holomorph of (G,⋅). In particular, we find that certain groups studied by T. Kohl, F. Dalla Volta and the author, and C. Tsang all yield examples of bi-skew braces. Building on a construction of Childs, we also give various methods for exhibiting further examples of bi-skew braces.