1. **State the problem:** We need to find which point lies on the perpendicular bisector of the line segment $ST$. 2. **Recall the definition:** The perpendicular bisector of a segment is a line that is perpendicular to the segment and passes through its midpoint. 3. **Analyze the points:** Since $ST$ is horizontal, its perpendicular bisector is a vertical line through the midpoint of $ST$. 4. **Identify the midpoint of $ST$:** The midpoint is exactly halfway between $S$ and $T$. 5. **Check which point lies on this vertical line:** Among points $W$, $X$, $Y$, and $Z$, point $X$ is closest to the midpoint and lies on the vertical line perpendicular to $ST$. **Final answer:** Point $X$ lies on the perpendicular bisector of $ST$. Therefore, the correct choice is **B**.