With my first tattoo it was with an artist that wasnt in my area, so everything was done through emails. He was very straight forward, said he charged $150 per hour, expected it would take about 4 hours for the initial sitting. He warned me though that if I was the sort who needed a lot of breaks or anything, then that would obviously take longer and cost more. It ended up being the exact time that he quoted, so it was the exact price he quoted.
With my second/third tattoos, the artist was in my town and wasnt as precise, and she basically said "it wont be more than 5 hours" and said she charged $150 for the first hour and $100 for the subsequent hours. So I brought enough for 5 hours and ended up paying less.
I wouldnt go to an artist who didnt at least give me a maximum. And if they tried to go above that on the day I just wouldnt go through with it.