Be sure to keep yourself well hydrated when you ride. Low blood pressure is good, but getting dehydrated can lead to low blood volume which drops your blood pressure even further, and can cause the dizzy or fainting thing when you stand suddenly. My blood pressure often seems exceedingly low after riding (101 over 61 at a doctor's appointment after a morning ride two weeks ago), and I've had the dizzy symptoms, so I did a bit of research. Google "hypotension" to learn more.

I do have to smile at some of the nurse reactions that kind of blood pressure gets. The last one was, "Is that natural or are you on a high blood pressure drug?"