Welcome to Fishlore.
First, you'll want to get him into a heated tank with a filter, at least 10 litres. Acclimate him slowly to the new tank by floating him in a cup with water from his bowl and adding a little tank water every 5 minutes until the cup is full.
What are you using to treat the tap water with? I would recommend Prime. It will help him during the tank cycling. Also change about 30-50% of the water daily until the tank is cycled.
If you can find products called Vita-Chem or Fish Protector or Garlic Guard those will help him out. He may simply feel bored or cold in a bowl and moving him to a tank with water of 78-80F and a filter will be good for that.
Bettas also like air bubbles to play with, and like to have a cave or two and some plants. Silk plants or live plants are best and for the caves, just check to be sure no holes are smaller than your thumb (Bettas can get stuck squeezing into small holes). Also check for any spots that are rough or scratchy. Betta fins snag and tear as easily (if not easier) than pantyhose.
If you are feeding him freeze-dried bloodworms, I would recommend soaking them in a little dish of some tank water to get them more plump before feeding them to him. 3 bloodworms, twice a day is what we'd recommend on those. They are so dry that they can cause constipation in Bettas. If you can feed him 3 pellet sized pieces of a thawed & peeled frozen pea once a week, that would be super for his digestive system.
Betta Food pellets (made by Ocean Nutrition) are good for him if you can find those. 3 pellets per meal, 2x a day.. just like the bloodworms.
http://www.drsfostersmith.com/produc...9&pcatid=15529