Think about it this way--fish constantly excrete waste through their gills in the form of ammonia. It's kind of like urine. In a closed system, there is no place for this ammonia to go, and no bacteria to reduce it into less harmful nitrate. If you change 50% of the water today, and then 50% tomorrow you are not removing 100% of the ammonia.
The only way to remove 100% of the ammonia is by doing 100% water changes unless your tank has been colonized by special bacteria. A lot of people will tell you very different things about when to change the water--the only way to know for sure is to use a test kit. You will need to get a test kit sooner or later anyway--be sure to get a liquid test such as the API Master Kit (http://www.fosterandsmithaquatics.co...54&pcatid=4454
). The pet store will usually try to convince you to get the dip strips, which are inaccurate and much more expensive per test.
If the ammonia test reading is anything above 0, the water should be changed. If you don't have a test kit, you can take your water to a fish store to have it tested for free. Once you work out how long it takes for your fish to pollute the water, you will know with certainty when to change the water.
If you aren't willing to get your water tested anytime soon, you simply have to play it safe and change 100% of the water at least every 3 days--washing out everything in the tank with hot water.
As for the comment about preserving bacteria--it's either one or the other, the cycled method or the 100% change method. There is no in between. Sadly, a 1 gallon tank is much too small to employ the cycled method, so you will need to do 100% changes.