Morrissey is here adapting for comic effect the proverb, "A bird in the hand is worth two in the bush". Which means that what you have is worth more than what you might get, or something.
Once he's changed the words about, the meaning is kind of obvious. It's possibly that "boy" is deliberately meant to contrast with "bird" (ie slang for a girl/girlfriend). "Bird" in the orginal saying means the kind that have wings.
"A boy in the bush" refers to the homosexual practice of having sex in the foliage of parks. "In the hand" is kind of obvious. Don't worry too much about why Morrissey thinks the former is preferable to the latter. He HAS to, or else the joke wouldn't work.