  We present a Lorentzian inversion formula valid for any defect CFT that
extracts the bulk channel CFT data as an analytic function of the spin
variable. This result complements the already obtained inversion formula for
the corresponding defect channel, and makes it now possible to implement the
analytic bootstrap program for defect CFT, by going back and forth between both
channels. A crucial role in our derivation is played by the Calogero-Sutherland
description of defect blocks which we review. As first applications we obtain
the large-spin limit of bulk CFT data necessary to reproduce the defect
identity, and also calculate the bulk data of the twist defect of the $3d$
Ising model to first order in the $\epsilon$-expansion.
