My blood pressure fluctuates a bit on prednisone, but usually within the normal range or a little lower. Whenever it (or my heart rate) is low I drink a couple of glasses of water and retest later and it's up again. A nurse told me once that dehydration can cause low blood pressure and/or low heart rate.

One of the symptoms of adrenal insufficiency is low blood pressure, and I sometimes notice a drop in pressure after starting a reduction. I take blood pressure almost every day to make sure I'm onto any possible adrenal crisis or insufficiency as the prednisone dose reduces. Currently reducing to 3mg and all is well. Make sure to keep up the fluids is all I can suggest.