the problem is he's in a bowl. bowls are great for cereal, but not so much for fish.
betas are tropical, so living in a bowl is like having to live in a small room with no toilet. not fun, would you be happy and active? of course not, and you'd probably end up getting sick. I highly suggest upgrading to at least a 2.5gallon tank with a filter and heater.
as for the white stuff, is it cottony? or is it more like the tips of his fins are turning white?
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it's columnaris, it's a bacterial infection. I'd suggest maracyn and maracyn 2.
although, keeping him in a bowl is just going ot cause it to come back... so its up to you if it's worth treating or not. the bowl is a death sentence anyway.
as for the guppies, as long as the tank is at last 10gallons, he'd be fine with them after treatment. bettas are NOT cold blooded killers and many people keep them with guppies. however I was refering to getting him his OWN tank.