Our bloke seems to be pretty efficient, and I guess we know our cows pretty well. One service is effective probably about 80% of the time for us. We've never had a good experience using PRIDs and so on; we always try if we've got one that's difficult and it hardly ever works out. So most of ours have a natural cycle and we call the fella in when we see them standing. So sometimes it's the same day, often it's first thing the following morning.
I should add that we don't have any need to use PRIDs in the normal run of things, so our experience of them is with cows that were proving tricky in the first place.
Most of our cows are beefy types, Angus and Hereford crosses. Some 1/2 Friesian, many 1/4 dairy, or less.
I think it's generally held to need to be more specific and harder to achieve a good hit rate with dairy types. I struggled to get my first Jersey back in calf, then realised that changes in routine upset her, so now I don't even get them served unless I know I can keep things the same for 5 weeks.
Also, our AI bloke knows which semens he has are high fertility. Some are single bull and he has some that are a mix of three, which he often uses if we have one that's proving difficult. Downside with the mixtures is you don't know who is the father, only one of three, but you get your cow in calf. Using mixtures wouldn't be any good for pedigree breeding stock, of course, but may be useful for a first calf if you've a heifer proving tricky. Calf would have to go for meat, of course.