The correct answer is option 3, bacteria. Monera is one of the five kingdoms of living organisms, and it includes single-celled organisms without a nucleus, such as bacteria.

Option 1, mushrooms, belongs to the kingdom Fungi, which includes multicellular organisms with a nucleus. Option 4, moss, belongs to the kingdom Plantae, which includes multicellular plants with a nucleus.

Option 2, yeast, is a bit tricky. Yeast can refer to both single-celled fungi (which would not be in the monera group) and single-celled bacteria (which would be in the monera group). Without further clarification, we cannot be sure of the exact type of yeast referred to in the question. Therefore, option 2 cannot be confidently categorized within the monera group.

To summarize, only option 3, bacteria, belongs to the monera group.