You don't need to bag your fish. I agree with what's already been said, that catching and bagging them stresses them more than just leaving them alone would.
Here's how I do my water changes. I do about 20-30% change once a week.
Using my gravel siphon thing, I empty the water out of the tank into a 1 gallon pitcher. (My tank is 15 gallons, and I empty out 4 pitchers full) Then I dump the pitcher. I do that four times. Then, I get a small plastic cup that I use for my tank, and add salt and water conditioner for the NEW water amount. (not all fish need salt, but mine benefit from it.) I put the cup into the tank. Then I fill the pitcher with tap water. Since I put the water conditioner in the cup, it's already treating the water as the water goes into the tank. So I fill the tank back up that way.
I'm no expert, I've only been keeping an aquarium for a few months, but that's how I've been doing it, and my fish are fine. Be sure to pour slowly, and if possible pour the new water on top of like a decoration or inverted plate so it doesn't stir up your substrate. (I aim my water for the driftwood I have in my tank.)
If you don't use salt, you might need to anchor the cup you put the water treatments into, maybe scoop some of the gravel from your aquarium into the cup to keep it from floating around. Or add the water treatments to the water right before you pour it in, one at a time ... but sometimes that can be hard to calculate, depending on what size container you use for water changes, and how the instructions for the treatments are done.