You'd want it in now if you can. After the corn plant has half a dozen leaves or so, it begins to stretch quickly between nodes, and you want that to happen just as the beans begin running. 6-8 leaves on the corn is usually when i would plant.
Also, Unless you have a long day of sun, and deep, fertile topsoil containing good ratios of the necessary compounds, I'd thin the corn just a bit. Part shade can cause the same affects as overpopulation, minus the root crowding. It's best to leave each plant plenty of room for best size. Long thin stalks will not support beans for long. I usually planted the corn in hills rather than drills, with 3 kernels in triangle formation (kernels spaced 10" apart) in hills on a 30" grid, left to grow (no thinning). And I only used 2 bean seeds per hill, as these are aggressive, and will grow until frost, even after the cornstalks are dead. I've never tried it in an area of any substantial shade.
If that's your only corn planting, I'd only put beans in half of the plot. That way you have backup in case of structural failure (you can prop bean vines back up and get a crop, not so with broken corn (if a grown stalk breaks, before the ear develops - If the corn leans from the root it can be propped).
I'd pull the mulch back just enough for the seeds, so they don't have to do the extra stretch for sunlight before beginning photosynthesis and mass building, although the mulch probably wouldn't stop a bean sprout.
Also, corn and beans are both heavy nitrogen feeders, but if fertilized too greatly the corn will lodge and you won't get a real crop. Let me know if I can expand on anything or add more.