How long can I store soaked beans before cooking?
It rather depends on the temperature of the room. Where I live, in the summer it gets hot and humid, and they shouldn't be out on the counter during the day, or they ferment.
In winter (like spring in the northern US, 45-70 farenheit) they can be out for two days with no problem.

My recommendation would be to soak overnight for morning use, or to soak during the day for evening use. It also helps to change the water every few hours, though this isn't critical.
If you refrigerate them with the water, you get an extra half-day. Refrigerating drained gets another day or so.

Either way, they should always be shaded, never in direct sunlight. 

If they do spoil, you'll know, as they'll have a sour/yeasty smell to them.