Ok but,
Cows don't require bees. The food that cows eat (wheat, grass, soy) either pollinates by wind or spreads by root. Soybean benefits, but doesn't rely on, insect pollination. Alfalfa is pollinated by bees, as are most forms of clover.
Cocoa trees are pollinated by midges, not bees. And the rest of the shake comes from the above mentioned cows.
Lettuce also self-pollinates, though again insects help. Commercially, they're not really used.
Tomatoes are commercially pollinated by shaking them, because commercial tomatoes are optimized for making food and are pretty shit at being plants.
Potatoes are basically the only major ingredient that is pollinated by bees. But that's basically never used by anyone growing potatoes, since potatoes also spread asexually by tubers.
Stuff in this pic that IS pollinated by bees: the sugar beets that are potentially in everything (edit: nope, that's wrong) but not the corn you can also use for sugar. Cucumber for the pickles. Some oil plants to fry in. Coconut or almond if you don't want cow milk. Sesame seeds on the bun.