I am so sorry being so late getting to you but I did not catch this post yesterday...
First I would have you read the Betta Care Guide and then let me make some recommendations about a proper care for this poor fish.
http://www.fishlore.com/Forum/betta-...d-first.0.html
He needs some nice clean surroundings. I would get a healing water conditioner like StressCoat for him since he is a bit fragile. Use it as the dechlorinating agent for the tap water. He needs to go into a
heated and filtered tank of at least 3 gallons but preferably 5 gallons or more.. Since the tank is not going to be cycled he is going to need to have frequent water changes.
You mentioned that he is in a bowl. Fin rot is a coolwater problem a lot of the time and since water in bowls is not heated he cannot get over it in the bowl.
He needs good nutrious Betta food - freeze-dried bloodworms, Hikari Betta Bio-gold pellets, freeze-dried Daphnia, freeze-dried Baby
brine shrimp (not an everyday food and the least nutritious). He needs some greens (the frozen pea treatment) to make sure that he is not suffering from constipation due to the cool water slowing down his metabolism. (the Frozen Pea Treatment Instructions are in the Betta Care Guide)
Staying at the bottom of the bowl is one indication that he is really unwell. Not blowing bubblenests is not necessarily the sign of illness but of being unhappy. Rapid gill movement and acting like he cannot breathe means that there is probably a water quality problem as well as illness involved. I would get a larger container, even if it is one of the big new plastic buckets at the Dollar Store. You can buy a heater for it and at least heat it for him and worry about the filtration when you can get a small tank. You will just have to do frequent water changes until then.
The absolute minimum at this stage is:
1. A new large plastic bucket (preferably white or clear) or container that has never been used for detergents of any kind. Unless you want or can go ahead and get him a filtered tank like a Hex5 or even a 3 gallon with a filter. Even a large Critter Keeper will be okay for a long-term home if you can get one. (large like 3 gallon size)
2. An aquarium heater that can be submerged and that has an adjustable thermostat. (NO preset heaters or small tank heaters - you have to be able to control the heat - no high/low needs actual degree settings)
3. A good healing dechlorinator/conditioner like StressCoat.
4. Good quality high protein Betta Food like freeze-dried bloodworms since he is having problems with fins he needs high protein foods or Freeze-dried Daphnia.
5. The frozen pea treatment.
Thank you so much for doing this for this little fish. He will be a good little buddy for you if we can get him better. There is a medication that you can get for his fins called Furan-2 but it would be better to see if you can get him into some nice clean water and conditioner and give him some good food. Be prepared to do a 30%
water change on him every day because he is not going to be in a cycled tank and the water will have to be kept especially
ammonia free for his healing. The heat, food, and clean water as well as giving him a larger area to swim will do wonders after a few days if he is going to be able to make it.
Welcome to our Board and please feel free to come back with questions and comments whenever you want to.
We would appreciate hearing a progress report on this little one and hope you stay with us.
Merry Christmas.
Rose
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. and i feel terrible about that. i am so glad that you are attempting to care for your beloved finned baby. i have recently lost a betta and know how you may be feeling right now. 
its a terrible thing. i am sry. and thank you for doing your part to protect our finned babies!
