Why would heart rate drop to mid 50's only when systolic blood pressure reading?

The systolic blood pressure number (top number) measures the pressure in the arteries when the heart beats (when the heart muscle contracts).

The heart rate (pulse rate) is the number of times your heart beats per minute.

Here are some more things to know about the correlation between blood pressure and heart rate.

There is no good correlation between pulse rate and blood pressure.
Measuring pulse rate does not indicate high or low blood pressure. .

A rising heart rate does not cause your blood pressure to increase at the same rate.
Even though your heart is beating more times a minute, healthy blood vessels dilate (get larger) to allow more blood to flow through more easily. When you exercise, your heart speeds up so the blood can reach your muscles. It may be possible for your heart rate to double safely, while your blood pressure may respond by only increasing a modest amount.

Taking your pulse can measure your cardiovascular activity and oxygen consumption but it is not a substitute for measuring your blood pressure.
If you take your pulse (measuring your heart rate) before, during and after physical activity, you'll notice your pulse will increase over the course of the exercise. The greater the intensity and the more energy the activity demands, the more your pulse will increase. When you stop exercising, your pulse does not immediately return to normal; it gradually returns to its resting level. The greater your fitness level, the sooner your pulse rate will return to normal. These numbers may be helpful to understand but they are not linked to your blood pressure.