Blood Test 1 week before the wedding

I had blood drawn on August 26th not even thinking about my Sept 10th wedding. Of course I bruised. I just left the wrapped bandage thingy on longer than normal. The bruise was gone within about 5 days. I think ice may work. Your makeup artist may have some tricks to prevent staining.

Can they take a blood sample from another less conspicuous body part?

Ice the first day, then apply heat. You can also cover it with makeup.

You can massage the area with your hand a few times a day and it will distribute the blood and get rid of the bruise fast.

OK, I admit this sounds like an old wive's tale, but I have used this trick regularly since I learned about it and it works. Applying witch hazel (sold over the counter near the rubbing alcohol) around the site as soon as possible after the injury (in this case, a blood draw) will prevent any bruising from appearing.