Skip the collar, especially if it is a shock collar.
First, never share any food from the table ever again. She knows she has succeeded in barking her way to the treats, so it is going to be a hard habit to break.
Work with her on training outside of meal time to. Does she know sit and quiet? When you sit down to eat, and she starts barking, give the quiet and sit commands. If she doesn't listen, ignore her. If she thinks she is getting to you, she will keep it up. You are going to have to put up with some noisy meals, but the training will pay off. It's a test of willpower.
Do things to tire her out before mealtime, like a walk or vigorous game of fetch.
My boys know not to disturb me while I'm eating, but lately we have been naughty and giving them little bits of food while we are cooking and right when we sit down at the table. Now they are starting to beg a little. I'm inadvertently training them to do this. I need to stop before it gets worse.