I used to take 6 of my 8 kids shopping with me on a regular basis so my wife could have some quiet time for herself. When the youngest was nursing I didn't take him with me because I'm not properly equipted. I have taken all 8 of my kids shopping many times, to give my wife a break and to teach them what I knew about shopping wisely.
I never bribed my kids to get them to be good. Then they misbehave so they can have the bribe. If you reward bad behavior, you get more bad behavior.
If my kids were misbehaving, I would talk to them or swat them depending on what the problem was and how severe the misbehaving was. My children stayed by the cart, but I would give them assignments like select a box of cereal you would like. If it costs less than 10 cents per ounce, then we can get it. All of my kids were allowed to select a cereal or a fruit or anything we needed. I showed them how to select the best fruit (ripe, right size, the thin skinned citrus, the best bag of potatoes, or carrots, etc). I showed then how to select the least fatty meat and what a good bargain was and what wasn't.
I viewed my teaching how to shop wisely was as important as teaching how to understand what they read. My mom taught me. I taught my kids.
Teaching your kids how to behave in a store is important. I think that because I taught them things while we were in a store they were less bored and therefore less likely to misbehave.
Good luck to you and yours.