Think alternator is bad

Don't know.
You would need to have both components tested. It could be a dead cell in the battery. Or a bad connection. If the alternator were at fault it should discharge when the engine is running and slowly go dead.

I just went thru same thing with my 2003 f-350 diesel. I hooked up my horse Trailor and drove to Von's parked went in came back out and truck was dead. I tried to jump it didn't work. Then over next two hours two tow truck Drivers hooked up to both batteries full power charge direct to my truck and would not start.
End story required two new batteries alternator and cilanoid discussed above. In other post. Also contributing to the cause was really badly coroded cables they looked good at the connection point but wher discovered to be coroded inside the tubing just above the end connections so bow it has all been replaced and I have had no trouble since. Hope this helps. Tanya

B sure to check the wire oink to the starter for corrosion and check the ground under the hood also your problem is one of those okay thanx Chris

alternator problem ,start engine the remove a battery terminal if engine stops renew the alternator

More then likely a bad cell in the battery, so it won't hold a charge, jump it and go to any auto parts, they will check the battery and alternator for free, I don't think it's the alternator, due to you drove it for 40 min with no trouble, if it was the alternator, the car would have turn off on you while driving it.Most of these auto parts will also install the battery for you for free.

replace the alternator,this is the problem,please rate thank you.

Welcome to the world of BMW's. return the car to the seller. you got a bad one. You got an electrical short draining the battery. Bring a blank check and sign it over to the dealer. They're going to have to run through the entire electrical system to find the short. That work alone is worth more than the a used up 2001 325i.

Sounds like the alternator is bad (not charging). If your battery is good/charged it should run until the battery is drained. If the battery is bad/not charged the car will die as soon as the cables are taken off as there is not enough juice to run the ignition system. If the alternator is good (but battery bad) the car would still run as the alternator makes power to run the car but becasue the battery is dead/drained there is no power to start the car (hense needing the jump). Have the alternator/charging system tested

check to make sure the alternator is charging the battery.crank engine while idling the alternator out put should be 13.5 volts to 14.5 volts. if not alternator is not charging the battery.if alternator is charging battery.the battery is weak.if its over 5 years old its more likely battery.if battery not old checks out good .replace battery cables..

you will need a new altenator and a battery