Consider the following passage from Alan M. Weinberg's book, Shelley's Italian Experience, which will help explain the significance of the "poor captive bird" metaphor:
A new, personal facet of Shelley’s Italian experience comes to the fore at Pisa with the composition of Epipsychidion. The subtitle of the poem addresses Shelley’s verses "to the Noble and Unfortunate Lady, Emilia V-----, Now Imprisoned in the Convent of-----." The ‘Lady’ to whom Shelley refers—the nineteen-year-old Florentine Contessina, Teresa (Emilia) Viviani della Robbia—had been confined by her father, the governor of Pisa, to the conservatory of St Anna, where she was obliged, under great duress, to await an eventual marriage to a favourable suitor. Francesco Pacchiani first alerted Shelley to the plight of Emilia. He spoke of the convent as a "miserable place" and arranged for Mary and Clare to visit St. Anna on 29 November 1820. Soon after, Shelley himself made the first of many visits and, within a short time, developed a deep interest in Emilia. Epipsychidion was probably written in late January and early February 1821, at what appears to be the height of the relationship, when the poet was attempting to win Emilia’s liberation by means of letters and a petition to the Italian authorities. Not surprisingly, Shelley was angered by the rigid laws and conventions of the Italian social system, and he considered Emilia’s situation as typical of the paternalistic tyranny which he had depicted in The Cenci, and which still prevailed in Italy. The possibility of being Emilia’s liberator reawakened his zeal for active engagement on behalf of those who were victims of society. (135)
Weinberg provides us with a contextual frame for the poem. What is interesting, however, is that this poem becomes as much a poem about Shelley's own sense of confinement as Emilia's. Emilia (Emily) actually turns into a liberated figure in the poem. The "poor captive bird" is a metaphor for both Shelley and Emilia.
It is also worth noting, as Weinberg does, that Shelley translated the first thirteen stanzas of Ode to Liberty into Italian, hoping that it would inspire her to rebel against her parents' rule. Shelley was clearly inspired by the Spanish Liberal Revolution when he wrote Ode to Liberty, as Weinberg points out (136). Let's take a look at the first nine lines of the poem and see if there is an intuitive or explicit thematic connection in Epipsychidion:
A GLORIOUS people vibrated again
The lightning of the Nations; Liberty,
From heart to heart, from tower to tower,
o'er Spain,
Scattering contagious fire into the sky,
Gleamed. My soul spurned the chains of
its dismay,
And in the rapid plumes of song
Clothed itself, sublime and strong;
As a young eagle soars the morning clouds
among,
Hovering in verse o'er its accustomed
prey.
The poet here certainly finds aesthetic pleasure in the revolutionary sprit; he senses people "vibrating" with excitement over the prospect of freedom. And we have the bird imagery in this poem, that of an eagle"soar[ing] the morning clouds among." It is especially interesting that Shelley took the time to translate thirteen stanzas of the poem to Emilia; Shelley must see political revolutions as macroscopic representations of smaller revolutions, such as the individual's revolt against familial tyranny, which he hopes Emilia will consider as a means to gain her freedom.
Weinberg, Alan. Shelley's Italian Experience. New York: St. Martin's P, 1991.