I suppose the sole point of actually floating the bag in the water is to match bag water temp to tank water temp. If you dont have a drip acclimation system in place, then it just becomes a convenient place to keep the fish while you perform the manual acclimation (removing bag water and replacing it with tank water).
The the point of removing a little and then adding a little is so that the adjustments in pH, nitrate, etc will be more gradual. The same thing is happening during drip acclimation except instead of there being a small and constant removal/adding, its happening in larger chunks that are spread out over longer intervals.
Drip acclimation is removing, for example, 3 drops of bag/store water per second and instantly replacing it with 3 drops of tank water per second.
Manual acclimation is you taking a measuring cup, say 1/4 cup, and removing that much bag/store water and replacing it with the same amount of tank water every 5 minutes for an hour or two.
How much is swapped, the length between swapping, and the duration of the total process will likely vary from person to person and is another debate entirely.
... and now that I think about it, both processes resolve the "sitting in their own ammonia" issue because old water that might have ammonia build up is being removed and then being replaced with cycled tank water that should be ammonia free.
Ive yet to have fish delivered to me in the mail or drive more than 30 minutes with new fish. I assumed that fish sent in the mail had something added to the water to deal with the ammonia build up. Maybe those far away LFS (holy schmoley, 3 hours!?) could add the same or similar to your bag?