I'm not sure if they can tell when you will ovulate by blood test, but I think they can tell round about when you might ovulate by the ultrasound. Blood tests are usually done to confirm that ovulation has occurred.
Just don't look! I NEVER look when they are taking blood. Plus I have crap veins, they are all "jelly" like the nurses always tell me. So I just have to put both my arms out and get them to try both.
Let us know how you go