I think everyone's situation is different.
I was on my own for 6 years before I met DP. He and I dated for 6 months before they were introduced to him, although I may have done it sooner had we been ready sooner (being both long-term single with very full lives, it wasn't the quickest-moving relationship initially).
My DC weren't vulnerable to a new relationship. We have been a single parent family since they were babies (twins) so they have not had to experience massive upheaval or the pain of a significantly changed relationship with one parent. By maintaining an active life while single, I didn't have to worry too much about them feeling 'neglected' when I went on dates.
The main thing for me was that they reached a point where they emotionally understood that DP was a welcome addition to the family unit, not someone who detracted from their relationship with me. To that end, introductions were very slow and piecemeal and the DC set the pace.
First meeting was outside on neutral territory with other people and plenty of opportunity for avoidance (for him as well as them) if it all got too much. He'd call in for coffee before dates and spend 5 minutes chatting. It was a while before he stayed over and a lot longer still before I would allow him to do any parenting. Roles such as reading a bedtime story were exclusively mine until I knew he was a long-term keeper and the DC were ready for it.
A few years later, we're still here as a family unit and my DC adore him.
I don't think women should sacrifice themselves on the altar of motherhood. It does children good to see their parents as well-rounded people who have their own interests outside the family. But if you're introducing a new partner, the main rule is don't rush it I think. If he's the right one, he'll be led by you and never make you feel you're not prioritising him enough.