The man walks down the road for half an hour at an average speed of 3 miles per hour. This means he covers a distance of (3 miles per hour) * (0.5 hours) = 1.5 miles during his walk.

He waits 10 minutes for a bus, which takes him back to his starting point at 3:15. This means the bus ride took 3:15 - 2:25 = 50 minutes.

We know that during this 50-minute bus ride, the man traveled 1.5 miles.

Now, let's calculate the average speed of the bus. We'll convert the time to hours:

50 minutes = 50/60 hours = 5/6 hours

Average speed of the bus = Distance / Time = 1.5 miles / (5/6 hours)

To divide by a fraction, we can multiply by its reciprocal:

Average speed of the bus = 1.5 miles * (6/5) hours = 9 miles per hour

So, the average speed of the bus is 9 miles per hour.

The correct answer is 9 mph.