Here is how I do water changes.
I turn off my heater and filter, I start siphoning the gravel until the desired amount of water is removed. In your case, remove water until you have left just enough water for your fish to swim, let's say the height of his body plus 1 inch or so. Then, fill your bucket with clean dechlorinated water (try to temperature match it, you can use your tank thermometer) and add it back in until you have filled it all the way up again. Then restart your filter and heater.
Yes, in the beginning, fish don't like this and will swim around frantic and hide... but they do get used to it and it becomes less of a deal. My guppies, for example, follow my siphon around and make it a pain.