This is a tough question and you have to use your best judgment but I would recommend waiting until you believe there is a chance that this could be a serious relationship before introducing your new partner to your children.
It can be very difficult on your children if you bring someone home that they happen to really like and then one day that person doesn't come around anymore.
If you truly believe there is a chance that this could become a serious long term relationship, then you will have to introduce your new partner to your kids at some point.
So, you found someone you like, you hit it off, and you've been dating for a while, when is the right time to bring them home and introduce them to the kids?
From the logistics of meeting people to date in the first place to how your new social life will affect your children, you've got a lot more to think about than you did when you were dating in your twenties.
You've spent all day at work then you have to come home, cook meals, pick the kids up from soccer practice, how do you even meet anyone to go out on a date with? You can find a little time at night after you put the kids to bed to get on the computer and meet some people in cyberspace.
Something fun like a trip to the zoo or an amusement park may be a good option.
In the days before the internet there were, and still are, groups and events where single parents can get together and mingle.
Check your phone book or local newspaper to find these groups or special events.