The short answer is, "you're not". I bottle from 25 to 150 bottles at a time, and the sanitizing process for that many bottles is daunting.
The bottles don't need drying -- if you feel the need, put a splash of sanitizer in a bottle, pour it out, then let the bottle rest (Star San 1 minute, K-meta 10 minutes) before filling.
As a beginner, I had a bottling conversation with a winery owner, who had been in the business, both working for others and as his own winery owner, for over 20 years. He laughed at the process I went through with bottles-n-corks. I spent a lot of time in the NY Finger Lakes during that period and sounded out other winery owners, and they all agreed.
If you are buying new bottles, they are clean. Same with corks -- wineries cut the bag and pour into the hopper. They are clean and in a sealed bag. If anything, the hopper is the dirtiest part of the process.
As I get bottles, I soak the labels and ensure they are clean, inside and out. They dry on the tree and go into clean cases, mouth down. There is nothing in the bottle for anything to grow on, and being upside down and the mouth sealed against the case, there's no dust. At bottling time I visually inspect bottles and then line 'em up.