I would teach the kids not to be so afraid of the bees. Unless they go around swatting at them, the bees usually won't bother them and they are going to be around bees for the rest of their life (hopefully). A yard without blooms/bees wouldn't be my goal.

But, if pretty flower -less vines is the goal, you might could use English Ivy. I've not noticed a lot of bees around English Ivy before (of course there is the snake and spider issue).

Akieba (sp?) It will bloom in early spring and smells great which attracts bugs for that time but that time doesn't last long. The rest of the year it's just a great looking - not harmful to what it climbs on vine.

Akebia does attract bees. Maybe(?) it's less attractive than some plants, but bees will still visit chocolate vine flowers. Also, Akebia (like the English Ivy I mentioned above) can be invasive. It is listed on quite a few invasive plant lists.

You know, any vine that has flowers will have bees and bugs. Heck, the white clover blooms that come with our yard (no matter how much we fight it) attract more bees than anything else. I used to be terrified of bugs when I started gardening. You know, work a second, scream and skreech a minute. I've gotten over it somewhat. I even like seeing snakes in the gardens I just don't touch them. Oh, my akebia only blooms for about 2 weeks in the spring yellow blooms that smell like honeysuckle. It been there for about 8 to 10 years and I've never had to control it from spreading and I've never seen new ones sprouting in my woods. Maybe because it's a cultivar of the chocolate vine and not the original species plant.
Come to think of it, it was having kids that got me over my bug-Itis. We have bug id books and critter id books and the kids have become quite good at researching and id-ing lots of things. Maybe that would be a better option than trying to garden without bees.