Voltage is at zero when jeep is running
 

On my 2001 cherokee, the voltage reads all the way down on the dash when shes running. Eventually the jeep runs out of battery and can't start. When I charge the battery and put it back in, the RPM jumps up to 1500 (Im assuming its so the alternator will kick on), and when I take a reading on the battery with the voltmeter, the voltage drops like .5 volts every 30 seconds, continuously. Upon shutting the jeep off, the battery has been drained and the jeep wont start.

Is this just case of a bad battery or alternator? I checked all the grounds and they seemed fine.

I suggest that you remove your alternator and take it to a auto parts store and have it bench checked. Sounds like it's toast.

Would a bad alternator cause the battery to drain so fast?

it's possible.

no it is not that, it isn't even charging the battery at all.

Just find where the wire comes of the alternator then use a multi-meter to test it, you should get 12+ volts off of it.

check the charging fuse or fuses, and most autoparts store you don't need to remove the alternator for them to test it for free, but sounds like not charging, when the engine running most of the electrical load come from alternator + charging the battery, with it not charging the battery has to take the electrical load and goes dead quickly running all electrical parts of the jeep

If it's charging you should read higher than with the jeep off. Take it to Advance, they can test it in the vehicle quite well with the little microprocessor based tester they have there, free and only a couple minutes, with a LED screen and printout of the diodes and voltages under load.

might not be able to drive it there if it's as bad as he describes.