Driving with a bad alternator is not recommended but as long as the alternator is at least putting out 12 volts it's charging at least somewhat.
So if the car starts all the time then it's likely okay to drive with the bad alternator but I would highly recommend getting a new alternator installed before you're left stranded with a dead battery.
If the alternator goes completely out and doesn't charge or produce any voltage at all then the battery won't charge back up and the vehicle will stall eventually once the battery drains down.
So it would be best to get your alternator replaced as soon as possible if it's bad.
Autozone will usually test your alternator and battery for free and if your alternator is bad it should be replaced soon.
If the alternator is completely bad then your car will not run for long.