We take our open cows to an A.I. facility about 25 miles from here. They also collect, process, and store our own (& purchased) semen for us.
We have paid between about $50 and 100 to A.I. a female + semen cost. This includes about $5. to 8. per day board for the cow--we take the cow "early" to the facility to be sure they catch the proper heat sequence...easier than hauling cow back a 2nd time.
No reputable A.I. Tech, Vet, or Facility will make any type of guarantee as to whether the cow actually gets fertilized. Lot of variables, timing of A.I., condition of semen, initial processing and storage of semen, thawing of semen, A.I. procedure, condition of cow, etc. Cows we have had A.I.'d have taken with one session. I've heard that any cow that is A.I.'d will get pregnant anywhere between 50% and 100% of the time...
Only way to be sure is to Ultrasound (not palpate--too many Vet skill variables here) after about 6 to 8 weeks after A.I. Also, can put a bull with the cow about 3 or 4 weeks or so after A.I....he is better judge of heat than a Vet is...lol.