You need to change the water because fish excrete a toxic substance called "ammonia" into the water. It comes out of their gills, their skin, rotting food, and fish poo. In small bowls like yours it builds up very fast and will poison and eventually kill them. The bigger the bowl, the less times you have to change the water. Changing a little bit of water will not work because it builds up much too fast, so 100% water change is necessary if you do not have a filter.
As for the bucket, it doesn't have to be big and just one bucket is fine. It should be big enough for you to change all of the water in his bowl. Just fill it up the day before you change the water.
For the water conditioner, a lot of people use SeaChem Prime: http://www.thereefshoppe.ca/images/prime.jpg
or the TopFin brand: http://pet.imageg.net/graphics/produ...64t300x300.jpg
Having a bowl is fine for him but it is a lot more work than having a tank with a filter, it is also a lot safer for your fish in case you are busy one day and cannot change the water. This is my recommendation but of course it is your fish and you can do what you want with him :)