You need to get test kits for ammonia, nitrites, nitrates, and pH. Yes you need to have these--especially the first 3. I can not stress this enough. These toxins can kill fish overnight, and you do not even know they are there without a
test kit. A fish can only be healthy and happy if the ammonia and nitrite levels are 0 and nitrates are 20 or less. Taking water samples to the pet store is just not good enough. If a fish is acting funny, the first thing you always do is test the water. But what if the pet stores are closed? Your fish could die because you don't even know what is wrong. Test kits are one of the most important things you will buy. Oh, by the way get the liquid test kind, not dip tests since they aren't accurate.
Of course, tests are fairly useless if you don't even have a filter, because you already know there will be high ammonia (which is the deadliest toxin) without anything to remove it. Here's how the
nitrogen cycle works in case you are not familiar with it: the fish produces waste (ammonia); bacteria grows in the filter which "eats" the ammonia and turns it into nitrites (also toxic); a different kind of bacteria grows which turns the nitrites into nitrates (not harmful until they reach large amounts); and then of course you do your weekly water changes to dilute the nitrates. Without a filter this cycle can not happen and the fish will die, I am sorry to say.
I am sure your Betta is a very sweet fish and I know you care about him and so please do what is best for him. Bettas can not live comfortably without heat and some room to swim around and clean water. Please get him at least a 5 gallon with heating and filtration. Then he will definately become much more colorful and active...just ask anyone who's moved a Betta into a bigger tank, they are so much happier.
By the way, does your betta have a name?