I agree with B. People need to control their exciting new feelings for a new love and not introduce them to children who do not understand adult emotions. They can bond with someone who doesn't stay in the picture, and then when that boyfriend leaves, it can increase insecurity for a child whose father has already left. (Same goes for reverse genders.) I think it's fine for kids to know that Mommy is going out with a grown-up friend for a grown-up evening, but Mommy should be driving herself to this date. If the kids meet someone in a big BBQ of all kinds of friends, that's different. But still, they shouldn't be learning this is Mommy's boyfriend.
A friend divorced 5 years ago. Her ex sought his bliss in another state and married very soon thereafter. The kids were confused. He also rarely keeps his visitation arrangements, skips vacations and so on. It's awful.
The mom, meantime, devoted herself to the kids and to big social things at the synagogue, with the religious school parents, and so on. So the kids had a big community of friends and saw that their mom had adult friends. About 3 years ago, a man she dated right after college looked her up, and they started dating casually, then more intensely, but only when his kids and hers weren't around (summer camp, visiting the other parent, at sleepovers). Recently, a they decided to be a couple and the kids met him as Mom's boyfriend. They had met once before, years ago, when the grandparents wanted to go to the large store in their town that the man manages - so they all were introduced to Joe, who went to grad school with Mom. That was it until the 3 year mark. I think she handled it beautifully, and the kids are enjoying time with him - because he goes to gymnastics with them, does stuff around the house, and goes to the restaurants they like.