"The Sick Rose" is a very weird poem, which makes us think that the speaker is a little weird too. There are lots of ways you could picture the speaker, but here's our take: he's kind of like a bizarre next door-neighbor. Sometimes he sings little songs about the plants in his garden; you've caught him doing this a bunch of times, and it always reminds you of a Disney movie.
One day you are watching him over your wall as he's picking some roses to put on his kitchen table. You notice that one of the roses is a little brown and you hear your neighbor exclaim, "O rose, thou art sick." That sounds normal enough, but then he starts going on about a magical worm that "flies in the night." OK, that's a little strange, but nothing you haven't heard from him before. But then your neighbor's song gets strangely sexual, and he starts talking about how the worm destroys the rose with his "dark secret love." As you stare in astonishment, your friendly neighbor turns around and says hello; he doesn't even look embarrassed that you've overheard one of the strangest things in recent memory. He says to you, "I can't get rid of these worms in my garden because they're too small to see."
OK that explains the "invisible part," but you're still wondering about that violent sexual encounter he describes. Then, as if he can read your mind, he says, "I really, really, really like my roses; when a worm eats them, I can't help thinking that the worm is destroying them. I really like poetry too, so naturally I like to write poems about it. It helps me deal with a situation that makes me sad."
When he finishes, he tells you to hold on as he quickly runs into the house. When he comes back, he has a huge stack of papers in his hands. He tells you that the book is a collection of illustrated poems he's been working on for children and asks if you would like to take a look. You decline, telling him you'll wait until you can get a copy on Amazon, but you think to yourself, "There's no way my kids are reading these poems."