I have 3 years old bitch, she started bleeding on 16th august,  we checked her progesterone on 20th august and it was 7.5 and vet said to mate her the following day aka 21st august. We introduced her to the male and he wanted to mate her but she refused and snapped couple of times, we managed to collect the semen and artifficialy insemenate her though. We were told to mate her again in two days. So after 2 days we brought her to the male again and now she was very interested and was flirting and flagging but male just sniffed/licked and not tried to mount at all. We were bringing her to him every day since then and always the same, she wants it but he doesnt. And i must say that all neighbourhood dogs are showing up in front of our house because they sense her heat and that leaves me confused.

Also, the dog we want to mate her with is very experienced and has sired more than 5 litters.
Bitch has never been mated before.

What do you think what are the chances of bitch getting pregnant with AI based on her progesterone?

It's impossible to say with just a single progesterone test, what was going on.  You really need a series of tests which identify when ovulation occurred (which can be different for different bitches).  You are looking for the jump or leap in numbers, not just one number.  So your progesterone test isn't much use...

I'd say that you took her too early the first time and she put the male off by snapping and he then remembered that and didn't want to breed her even when the time was right.  This would be more common if he was inexperienced, but I guess it could happen with a sensitive male as well...

Add to 1234's answer would be the fact that something may smell different once a bitch has been mated successfully - my experienced male wasn't interested when we'd put him to the bitch, if she'd been mated a day or two before,  and there was a pregnancy starting.   Maybe the AI has worked!!  At least you got something in there so when she was right to conceive, she did.

I would agree with 1234; you took her to the dog too soon and she told him off too firmly, so now he's not going to mate her even when she's ready.

If she does turn out to be pregnant you'll need to tell the KC (if you're in the UK) that the pups were conceived by AI.

Presuming your progesterone result is in nmols, you have mated several days too early.