Step 1: Understanding nitrification.
Nitrification is a biological process in which ammonia (NH$_3$) present in soil is converted into nitrite (NO$_2^-$) and then into nitrate (NO$_3^-$). This process is essential for making nitrogen available to plants.
Step 2: Two-step process of nitrification.
In the first step, ammonia is oxidized to nitrite by \textit{Nitrosomonas}. In the second step, nitrite is further oxidized to nitrate by \textit{Nitrobacter}. Both steps require aerobic conditions.
Step 3: Analysis of options.
(A) Nitrosomonas and Nitrobacter: Correct — These bacteria carry out the two sequential steps of nitrification.
(B) Azotobacter and Rhizobium: These are nitrogen-fixing bacteria, not nitrifying bacteria.
(C) Pseudomonas and Bacillus: These are mainly decomposers and denitrifiers.
(D) Clostridium and Thiobacillus: These bacteria are involved in anaerobic processes and sulfur oxidation.
Step 4: Final conclusion.
Since nitrification occurs through oxidation of ammonia and nitrite by specific bacteria, the correct answer is (A) Nitrosomonas and Nitrobacter.