What is the problem you're trying to solve?
I don't quite understand the issue here.
50% of a 20 gallon tank is 10 gallons, actually maybe 8 or 9 since you have gravel and decorations I assume.
So, that is 3 trips with a 3 gallon bucket, or better yet 5 gallon bucket with only 3 gallons in it so it doesn't slosh, if you can carry it. Dechlorinate in the bucket or even in the tank between buckets. I drag an 18 gallon bucket with 10 gallons in it across one or two rooms, and it is geting old, hurts my back.
BUT, it sounds like you have not been changing water regularly??
If so STOP.
Your tank parameters may be very, very different from the tap water now (like pH, GH, and KH) plus other stuff we cannot measure. Using spring water just means that the difference will be that much bigger. Some bottled water can have high phosphates and may create algae.
Better to spend your money on a bucket and some basic dechlorinator! I use stuff that takes out chlorine, nothing else, you might want to get something that removes chloramines too, But "bacteria", "slime coat", and "stress relievers" are unnecessary, IMO. And keep a big towel on the floor as you pour, and one on your shoulder, too.
You can hurt fish at this point by doing a large water change, with either tap or bottled water. Say, for example, the salt level of the tank had risen slowly as you topped off after minor evaporation with tap water that has minor salt levels. A sudden change in the salt level would be sort of like opening a window in an airplane as the osmotic pressure changes suddenly (remember how the heads explode in space movies?) It's just not a nice thing to do. This change won't be that drastic, but it could do damage in some cases.
So, start by doing small changes, frequently, like every day or two. You can practice math as you do it....(walking to the blackboard...)
How many 10% water changes will it take to get a 50% change effected.? If you answered 5 changes you are wrong, some of those changes took out the water you just added the other day, right?
1st change, replace 10% leaving 90% old
2nd change replace 10% of above, leaving 81% old = .9 x.9
3rd change, replace 10% of above, leaving 72.9% old = .9 x.9 x.9
and so on until 50% of old is left.
Takes 6 or 7 changes. (.9 to the 7th power is .478 )
After you have gotten to the 7th 10% change, you can begin doing 50% changes, weekly would be nice.
