It would be preferable, if at all possible, to check with your doctor about scheduling the blood test for immediately before or immediately after Shabbat.
Should a situation arise in which there is no alternative, please consult a Yoetzet Halacha Fertility Counselor to clarify how best to proceed. (This is a free service, details
here.).
Behatzlacha with your treatment!
This response was updated on 13 April, 2021.