Yes, gills can have bones.
Gills are supported by structures called gill arches. These arches can be made of either bone or cartilage, depending on the species of fish.
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Bony Fish: In most bony fish (Osteichthyes), the gill arches are indeed composed of bone.
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Cartilaginous Fish: In cartilaginous fish like sharks and rays (Chondrichthyes), the gill arches are made of cartilage.
Therefore, while not all gills have bones, many do. Whether a gill has bone or cartilage depends on the type of fish. The reference excerpt notes that the gill is supported by "a cartilaginous or bony gill arch".
