First of all... don't feel embarrassed to ask someone a question. As my husband says: "What's the worst they can do? Shoot us?" Brings things into perspective, huh?
Secondly, I would be just as picky as you think they will be. Ask them if they will let you try with blood draws, IV, IM, SQ injections, watch REALLY closely during surgeries (and talk through what they are doing-- "now I am making the first incision through the skin... now I am searching for the linea alba... now I am using the spay hook to retract the uterus, which I will follow to locate the ovary in order to detach the ovarian ligament from the body wall..." etc), calculate drug dosages, fluid dosages, etc. Explain radiographic and serologic findings. Teach you how to read a fecal float and a urinary cytology (and how to collect samples and set up the slide). Explain palpation techniques. Ask leading questions about next steps, allow you to explain treatments to clients.
Get the picture? If a Dr. is going to let you come in and just "observe," you don't get the "experience" part of the deal.
You need a set of all the different sized syringes... learn how to hold each with one hand and draw fluid out of a bag, inject fluid into the bag, empty air from the syringe. You need a set of lines to learn how to prime them to prevent air emboli.
That experience is what will get you into vet school. I am smart AND I have the technical talent to back it up. Look for a big Specialty practice in the area (I drove 45 minutes for mine- in SoCal, even), or find an emergency clinic. I worked swing shifts so that my job didn't interfere with my school, AND, bonus, when it wasn't busy and all the laundry was folded, I was put to work maintaining IV catheters, drawing blood samples from BG curve cases, giving treatment injections, etc.
If you're into large animals, get a few ride-alongs. With large animals, it depends on the vet- they are less likely to let you do procedures, since the owner is usually standing right there. But, you can watch lameness exams, radiograph set-ups, oral or nasal gastric intubations, castrations, vaccinations and blood draws, rectal palpations... and then ask all kinds of questions while you are on the way to the next farm- which restraint methods do you prefer? which drug combination do you use for chemical restraint? different ones for different situations? why? you actually CAN and absolutely OUGHT TO ask "why."
OK, I'm getting down from my soapbox- the view really is pretty nice from up here, though... think I'll go look for another one to climb onto!
J