Roman Catholique Military Ordinariate
-Canada-
Ordinariate militaire catholique romain
Each Eparchy may handle the procedure differently per its eparchial needs, but, yes, in short, the eparchial bishop seeks the bi-ritual indult from the Holy See after both the Latin and Eastern Bishops (or the Latin religious superior) agree (actually the bishops issue the nihil obstat), and the Eastern bishop decides that the Latin priest’s ministry would benefit the Eparchy.
(Dcn John Moltavo, The Byzantine Forum)
When an Eastern deacon, endowed with bi-ritual faculties or adaptation of rite, serves a Latin diocese, he may carry out the functions of the Latin deacon during the Holy Mass, administer baptism, and assist in the marriages of Latin Catholic (p.44)
Salachas, Dimitri and Krzystof Nitkiewicz, Inter-ecclesial Relations Eastern and Latin Catholics: A Canonical-Pastoral Handbook, Eng. ed. CLSA, Washington, 2009.