I think that the appropriate period of time depends on the relationship itself. If it's serious and it's time to start talking about & planning more of an everyday type life together, the kids should probably be introduced and included. If it's just for some lighthearted fun, leave the kids out all together. And then there is the all-in-between.
I also think that the age and personality of the kid/s are other factors.
Better to wait a while. Make sure its a dude you want in your life for the long term. It's damaging to young children to see short term men in their mother's lives and older children are just resentful and expect your new boyfriend to just go away eventually when you decide to end things. When you're sure and comitted then introduce. My two cents.