OP, do you have a family history of Factor V? If so, you are spot-on to be cautious. I had my test at a regular lab; it was about $300 at the time, but that was ~10 years ago. You might try calling LabCorp to see if they can give you an idea on the cost.
I have Factor V; my mom had it as well. Her dr recommended I get tested, and my oncologist thought I was nuts til it came back positive. I found out in my mid-40s. I was on BCPs for about six months in my early 20s and quit because I kept having leg cramps. Glad I read the warnings, because I also had polycystic ovarian syndrome and that was the standard treatment at the time. Docs kept recommending I take them and I’d mention the leg cramps and they thought I was overly cautious. My dad has a rare clotting disorder (Proteins C and S) which one of my sisters inherited; my other sister also has FV. Neither of our brothers do.
I have a 25 yo nephew who is FV positive (son of my sister with FV) and he has been declined for life insurance, as he threw a clot after surgery for a torn ACL.
I’ve had a big life insurance policy since before the diagnosis - they didn’t check for Factor V back then. They have never come back to re-rate me. I make sure those premiums are paid on time! 
Both my sons are negative; they were tested several years ago.
This stuff is why noone in my family wants to do 23andme.