Thou still unravish'd bride of quietness, (line 1)
The innocence of the urn is connected to sexual purity with this line. The point is that the urn is married, but still chaste. The urn exists in the middle between innocence and experience. Its purity is not child-like – it’s a "bride," after all – but it is virginal nonetheless.
She cannot fade, though thou hast not thy bliss, For ever wilt thou love, and she be fair! (lines 19-20)
Just like the urn, the lovers exist smack in the middle of innocence and experience. They have strong sexual desires but haven’t yet acted on them. Humans have always found this state to be especially poignant and attractive. The speaker thinks he has found the way to have the best of both worlds.
And, happy melodist, unwearièd, For ever piping songs for ever new; (lines 23-24)
The musician demonstrates a kind of artistic innocence. He’ll never get sick of his songs, because he’s always playing the same song for the first time. It’s like being able to go back and experience your favorite song again for the first time: over and over.