I have a 14 yr old daughter and I've had full custody since she was 6. Luckily, she loves going to my mom's on the weekends as long as she doesnt have sports/tournaments, so I have coverage there when I need it. However she is the one that makes the decision on going there as I would never force her to so I could see a chick.
My stance is simple- I would have to see a lot of light at the end of the tunnel with a chick in order for my daughter to enter the equation. My last LTR and I dated almost 5 months before she was ever around my daughter. There is no sense in bringing a kid into the mix unless you are sure the relationship is going somewhere. It can get messy and confusing.
My other requirement is this- my daughter comes first and foremost. Dont like that? Tough. Cant deal with that? Cya. I dont have time for the drama. I walked away from an almost 3 year LTR and engagement at the drop of the hat because she internally had a problem with me having a daughter that she couldnt overcome (she was 12 yrs younger than me, never married, no kids).
I also have rules on the flip side- If/when I would happen to introduce someone to my daughter I would make sure that my daughter was 100% respectful to the person. She is a great kid, loves sports, very easy to get along with......but I would make sure that she didnt do anything to thwart the relationship either.
If the woman you are dating isnt controlling, doesnt have insecurity issues and is fine just being the cool person and "friend", it should work very easily. Its when the woman starts being bossy, controlling, wanting to be your kids disciplinarian (not speaking from personal experience here but from what I have witnessed through friends) it starts to deteriorate very quickly.
At 40 yrs old, dating mainly 26-35 yr olds, I screen very efficiently so that this doesnt become a problem. So far there has only been one person introduced into my daughter's life from my dating life and if there is another, you can bet that it has been discussed on both ends, by all three parties before it happens and there is a good chance of it being a long lasting relationship first.