Soren,
I can relate to your issue, especially the dizzyness when standing up quickly and the tired feeling. I take a beta blocker - Toprol xl for my heart as I had quadruple bypass
surgery back in 2004. I've never had high blood pressure and in fact my BP has always been on the low side. My Dr. prescibes the Toprol to me so that my heart beats more efficiently and requires less oxygen to it. The downside of it is it makes my B/P and heart rate a little low. I did get him to lower the dosage though. I also experience times on my Speedmaster where I don't "feel" 100% right and comfortable and I tend to take it short and easy on my bike at those times. Like you, I try to stay well hydrated before and during rides which increases my body's total fluid and blood volume and lessens the effects of low B/P and that feeling of being shocky.
Bob