**Explanation:**

A Wheatstone bridge is a circuit used to measure unknown resistance by balancing the bridge. It consists of four resistive arms, with the unknown resistance connected to one of the arms. The bridge is balanced when the ratio of resistances in the arms is equal to the ratio of the bridge supply voltage.

The sensitivity of a Wheatstone bridge refers to its ability to detect small changes in the unknown resistance. It is influenced by several factors, as mentioned in the options:

**a) Galvanometer current sensitivity:**
The galvanometer is the measuring instrument used to detect the imbalance in the bridge. Its sensitivity refers to its ability to detect small changes in current. A more sensitive galvanometer will be able to detect smaller imbalances in the bridge, resulting in higher sensitivity for the Wheatstone bridge as a whole.

**b) Galvanometer resistance:**
The resistance of the galvanometer affects the current flowing through it. A higher resistance will result in a smaller current, while a lower resistance will result in a larger current. The sensitivity of the bridge is affected by the galvanometer resistance because the current flowing through the bridge arms is dependent on the galvanometer resistance. Therefore, the galvanometer resistance plays a role in determining the overall sensitivity of the Wheatstone bridge.

**c) Bridge supply voltage:**
The bridge supply voltage is the voltage applied across the bridge circuit. It determines the current flowing through the bridge arms and affects the sensitivity of the bridge. A higher supply voltage will result in a larger current flowing through the bridge arms, which can increase the sensitivity of the Wheatstone bridge.

**d) All of the above:**
All of the mentioned factors - galvanometer current sensitivity, galvanometer resistance, and bridge supply voltage - influence the sensitivity of the Wheatstone bridge. Each factor plays a specific role in determining the overall sensitivity of the bridge. Therefore, the correct answer is option 'D' - all of the above.