I'd be cautious of sealing up your well pump. You might need easy access to it at some point. You could set in a threaded pipe collar and cap there. It closes it off, and is easy to unscrew the cap to access it if you need to.

If you want to use bleach, you would need to apply it regularly for it to work as a treatment, it does not work as a preventitive. If you have moisture/humidity problems in your basement, check into utilizing dehumidifiers.