@Bi-Polar Bear,
I've had that when I switched bp meds. In my case, I took my bp immediatedly and it was quite low. Looked at the paper that comes with the meds, and it mentioned dizzyness. Also like yours, the dizzyness went away when I waited it out, and diminished happening when I kept taking the pills as prescribed (Yes, I saw my doctor, she said it was common).
It happened again with the pills I'm on now, which I figure are too strong and I need to see the doc again... though as I've kept taking them, the reaction has waned.
So... what... a) talk to the doc, b) follow your bp (maybe you already do).