I don't recommend keeping a betta in a bowl. These small bowls won't cycle, and the temperature doesn't stay stable. When you said the bowl was bare, do you mean no gravel or decorations? In a setup like this, there is no media for any good bacteria to live, so no cycle was taking place, although a bowl most likely won't cycle anyway. Bettas that live in bowls often contract diseases, such as finrot, or fungus, because the conditions in the bowl are not good, and the betta gets stressed from the temperature and ammonia fluctuations.
Bettas need a tank with a heater and filter like any other fish. I would get a 5 or 10 gallon tank, and a sponge filter. A small airpump can run the sponge filter, and a gang valve can lessen the airflow going through the sponge if the filter creates more current than the betta is confortable with. For a 5 gallon tank, you'll need a 25-watt heater, and for a 10 gallon tank, you'll need a 50-watt heater. Set the temperature to 80 degrees.
The betta will like some places to rest and hide. Put in some silk plants. Plastic plants may snag their fins, but I've had good luck with silk plants in betta tanks.
This heated, filtered tank will be an excellent home for a betta, and you'll be able to keep one for much longer than a few weeks!