How do we stop our new kitten bugging us when we're eating?

So shut her in another room when you eat!

Get rid of that mooch cat.

Best way is to feed the kitten before you eat and confine the kitten in one room (like your bedroom) while you are eating. When you are finished the kitten can come out as you are cleaning up the dishes, etc.

Every such critter is an individual with it's own agenda. Your little sweetie needs a place of her own - called a portable kennel - to chill in during mealtime. And yes, for the first few days, she'll howl and fuss. I mean, she's a cat! They learn, but slowly. Be patient and love her. Never hit her, and hissing at her does NOT help.

She is hungry and wanting your food.

If she is a growing kitten, she needs 3 full sized meals a day. She is stalking your plates and not getting the message because she is hungry.

Put it in another room.

tie it on a leash lolz