4. It is forbidden for an animal to go out [into the public domain on Shabbos] wearing a bell, even if it is muffled and does not ring (1). This applies even in a city that has an "Eruv" (2). It is, however, permissible for an animal to go out to a courtyard with such a bell (3). Nevertheless, if it is not muffled and rings, an animal may not wear it even in a courtyard (4).
(1) Even if it was not considered a burden, it would still be prohibited, because when one sees an animal with a bell around its neck, it looks like the owner is on his way to sell the animal in the markets on Shabbos. This type of prohibition is called "Ma'aris Ayin," and forbids doing anything that others might construe as a transgression. Other authorities claim that even without this prohibition (for example, it was an animal one wouldn't be going out to sell), the bell around its neck would still be considered a burden, and thus it would be prohibited to allow the animal into the public domain on Shabbos. (see Mishna Berura 305:43).
(2) An "Eiruv" is an enclosure consisting of a series of poles or the like, with wire or string pulled tight over the top of them. It turns the area enclosed by it (sometimes even a number of neighborhoods), into a private domain ("Reshus HaYochid"), thereby permitting carrying within it.
(3) The concern that people might think the animal is being led to the market for sale, only applies in a public place, not a private courtyard (It would apply in public place, even if carrying there on Shabbos is permitted). It should be noted that the prohibition against allowing one's animal to carry a burden on Shabbos, only applies to a public domain, and according to some, even to a Carmelis, but not to a courtyard, even if it is prohibited for a human to carry there (for example, if it didn't have an "eiruv chatzeros") (Mishna Berura 305:43).
(4) As we've seen, it is rabbinically prohibited to play a musical instrument on Shabbos, because it might break and one might inadvertently repair it, thereby violating Shabbos. According to many authorities, this prohibition applies to any object that is specifically designed to make a sound, such as whistles, bells, etc.