Hello, congrats on the new fish!
For an unfiltered 1 gallon bowl, I'd do full 100% water changes every other day or so, just remove your guy and out him in a cup, rinse everything, then refill with dechlorinated water, accumulate your guy and your good to go
Another option is, if you have a siphon small enough, just do a 50% PWC and get all uneaten food/waste out, then a 100% change once a week. Don't need to remove him for the PWC, though you may have to remove the decor to get in there and get the stuff out...
Hope this helps