Bryant could have a couple different themes in this poem. I think the strongest theme that you could support with archaic words would be in reference to religion. The first mention of God or a "higher being" would be in these lines:
"There is a Power whose care Teaches thy way along that pathless coast,-- The desert and illimitable air,-- Lone wandering, but not lost."
Like the bird, he too is alone in the world trying to find his way. He needs guidance as well--just as the bird needs help finding his way along the coast to wherever he is heading. But the key in this stanza is the last line. He and the bird are both alone, wandering, but they are not lost. They do have a Power that is guiding them safely through their lives. Bryant ends with assurance that he will have support when he needs it, just as the bird had guidance. This ending gives both the reader and the author/speaker confidence that all will be fine if he follows his guidance.
"He, who, from zone to zone, Guides through the boundless sky thy certain flight, In the long way that I must tread alone, Will lead my steps aright"