It's happened. You can have just one manic episode later in life and then never have another one, but that wouldn't be very common. I don't know about depression.

Your doctor's belief that bipolar burns itself out is very controversial. Numerous studies have not proven whether it worsens or improves with age. Many professionals believe in a theory called "kindling", which means that the pathway burns deeper, so to speak, with each episode. That's not proven either.