What is the genre of Poe's poem "The Bells" ?
Broadly, the genre is poetry. Subcategorized, the genre is an "ode." An ode is something akin to a song; odes have a lyrical meter that can almost be sung. (Without too much effort, you can sing it to the tune of "Hark the Hearld Angels Sing." )
Futhermore, odes typically embrace a subject of a grave nature; the topic is always serious, never comedic (in a true ode.) The form of an ode is also set; the stanzas adhere to a pattern throughout. In this case, AAA, BB, CD, CD.
The subject is always elevated, as is the case here, where, in the course of four stanzas, the speaker of the poem reflects on his youth, his young adulthood, middle-age, old age and impending death.
Poe's poem meets the criteria of an ode on all these fronts.