this morning I went out to my accord and the battery was died so I jumped it and drove it to work (30 min drive) parked it and unplugged the battery just in case.

got it home and left it pulgged in to see what would happen. Checking to turn off all lights, every thing, also took out my after market radio. Then came out next morning it was died. I then jumped it drove to part store and tested the system. It said that the alternator is bad.

Why would it be bad if the car runs and is drivable. but when it sits it drains the battery? any ideas?

 

The alternator is probably only charging at higher rpms, not so much at idle, and is probably not adequately charging the battery, which is horrible for your battery. I would buy an alternator, and if the battery still dies get a new battery.