  We showed that the SLE bubble measure recently constructed by Zhan arises
naturally from the conformal welding of two Liouville quantum gravity (LQG)
disks. The proof relies on (1) a "quantum version" of the limiting construction
of the SLE bubble, (2) the conformal welding between quantum triangles and
quantum disks due to Ang, Sun and Yu, and (3) the uniform embedding techniques
of Ang, Holden and Sun. As a by-product of our proof, we obtained a
decomposition formula of the SLE bubble measure. Furthermore, we provided two
applications of our conformal welding results. First, we computed the moments
of the conformal radius of the SLE bubble on the upper half plane conditioning
on surrounding i. The second application concerns the bulk-boundary correlation
function in the Liouville Conformal Field Theory (LCFT). Within probabilistic
frameworks, we derived a formula linking the bulk-boundary correlation function
in the LCFT to the joint law of left and right quantum boundary lengths, and
the quantum area of the two-pointed quantum disk. This relation is used by Ang,
Remy, Sun and Zhu in a concurrent work to verify the formula of two-pointed
bulk-boundary correlation function in physics predicted by Hosomichi (2001).
