To solve this problem, we can use the concept of average speed. The average speed of an object is calculated by dividing the total distance traveled by the total time taken.

Let's assume that the total distance traveled by the bus in one hour is D km.

- The speed of the bus excluding stoppages is given as 54 km/h.
- The speed of the bus including stoppages is given as 45 km/h.

We know that speed is calculated as distance divided by time. So, we can write the following equations:

- Speed excluding stoppages = D / (total time excluding stoppages)
- Speed including stoppages = D / (total time including stoppages)

Since the distance traveled is the same in both cases, we can equate the two equations:

D / (total time excluding stoppages) = D / (total time including stoppages)

We can simplify this equation to:

(total time excluding stoppages) / (total time including stoppages) = 54 / 45

Now, let's solve for the ratio of the total time excluding stoppages to the total time including stoppages:

(total time excluding stoppages) / (total time including stoppages) = 6 / 5

This means that the total time excluding stoppages is 6/5 times the total time including stoppages.

Now, we can calculate the time spent on stoppages per hour:

Total time excluding stoppages = (total time excluding stoppages) + (time spent on stoppages)

Since we know that the total time excluding stoppages is 6/5 times the total time including stoppages, we can write:

(total time excluding stoppages) = (6/5) * (total time including stoppages)

Substituting this value in the equation for total time excluding stoppages, we get:

(6/5) * (total time including stoppages) = (total time excluding stoppages) + (time spent on stoppages)

Simplifying this equation, we get:

(1/5) * (total time including stoppages) = (time spent on stoppages)

Since we are looking for the time spent on stoppages per hour, we can conclude that the time spent on stoppages is 1/5 of an hour, or 60/5 minutes.

Simplifying this value, we find that the bus stops for 12 minutes per hour.

Therefore, the correct answer is option B) 10 minutes.