You can store soaked, uncooked beans with or without the soaking water. I always store my beans without the soaking water because they last longer and it’s less effort.Here's how you do every method.
How to store soaked beans WITHOUT the soaking water
To store soaked beans, remove them from their soaking water and dry them thoroughly.
Once dry, put them in an airtight container and store them in the fridge.
The beans will be good for 4-5 days. If you want to keep them longer, you can freeze them.
How to store soaked beans WITH the soaking water
To store beans in their soaking water, the most important thing is to remember to change the water regularly (every 12 hours). This stops anything nasty from building up in the water.
Optionally, you can add a splash of vinegar to the soaking water to make it less hospitable for microbes.
If you plan to soak the beans for any longer than 24 hours, you should keep the container in the refrigerator. This is especially important during the summer when the air temperature is warmer.For less than 24 hours the beans will be fine on the counter.
Notes
For information on storing cooked beans (and how to freeze your beans), check out the full post above.