Fungal Infection
The picture at left is not of a betta, but it is a good depiction of what a large fungal infection looks like.
Symptoms: Betta has white cottony like patches on its body or head. He may be less active, may have stopped eating, fins may be clumped, color may be pale.
Treatment: There are lots of options for treating fungal infections. One that I've used for minor fungal infections is Mardel Maroxy, which is a liquid dropper medication. It's worked well when I've seen faint signs of cotton-y patches on bettas.
Do a full water change. I would probably try Fungus Cure by API just because I trust that brand.You can also try Jungle Fungus Eliminator; water should have a nice gold color if you use the yellow crystals; it shouldn't be too dark. Do not overmedicate! Change water every third day and add a new dose of same medication. Continue until all fungus has disappeared. After that you might try continuing with something like the Mardel Maroxy for a while to prevent any left-over fungus from coming back.
One my bettas get a fungal after we had a really bad snow storm which I think affected the tap water. This can happen anywhere, and I was advised to use spring water from the grocery store while I was treating him, and it worked. You might try that too if you think your tap water could play a factor.