The top number (systolic pressure) is considered normal if it's between 90 and 120. The bottom number (diastolic pressure) should be between 60 and 90... some sources say as low as 50 is fine.
Now... what is considered 'normal' is not necessarily normal for everyone. In health care, we look at trends... like what's the person's BP normally, and what is it now. If your girlfriend normally runs 120/78 for example, and now it's running 105/65, she may want to drink more fluids and speak with her doc.... but if she normall runs 110/68 or something, then I wouldn't get to worried. I have run as low as 78/56 and was perfectly fine.
As far as getting dizzy when standing... that's something called orthostatic hypotension
. The EMT's answer explained it perfect. If you have a BP cuff at home, you can see if she's experiencing this by taking her BP laying down, having her sit up and take it again as she sits, and take it once more when she stands. Wait 2 minutes between each pressure. If the top number drops by 15 or more mm/Hg, then she is experiencing orthostatic hypotension. It's nothing too dangerous as long as the doc rules out an underlying condition, just advise her to change position slowly to avoid fainting