I've been playing with various arrangements of this for several years now. Bush beans will be no problem planted in front -sunny side- of the corn.
Only wrinkle is when you want to hill the corn. If you can wait until corn is hilled once, and you don't need to hill again, you can pull the soil up along the row, THEN sow your beans about a foot in front. Otherwise, leave sufficient room to drop shovelfulls of soil to hill the corn with without burying the beans.
Pole beans have variously pulled down the corn when variety of corn is too short/wimpy and beans is too vigorous, blocked pollination, or kept on growing after corn was harvested, forcing me to leave the stalks standing to eventually get moldy and weak and fall over. Still trying different combinations and timing for that one, but late maturing extra tall field/dent/flour corn and beans meant for dry shelling seems to work out the best.
I have been more convinced of growing peas and fava beans in the same bed where corn will go in later, leaving sufficient row space in between pea rows. No fava beans this year, but I left trenches between pea rows to plant the corn so I can hill with soil from the raised pea rows, but it's still too early in the experiment to tell if this is going to work.
Yes, and like Lindsay said, go with blocks rather than long rows of corn. If you didn't have the corn already growing in cups, you could stagger the planting times -- corn, beans, corn, beans. I'm trying to delay some of my already started corn by keeping them in the cooler outside space while the ones I want to hurry up are inside under the lights.
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