It takes me less than an hour from start to finish to bottle beer. My bottles were rinsed well when I stored them. I get them out, quick look in the bottom up at the light on each one as I sanitize them. I used to dunk them in Star San but now I have one of those pump things (forget the name), they are like 15 bucks.
To answer your question though I used to use the dishwasher to sanitize them. Never had any problems doing it that way except waiting on the dishwasher. I would just put them in there, no soap. Hi Temp Wash>Sanitize>Start.
After you bottle enough times it gets easy, you develop a process. A lot of homebrewers go to kegging because they can't get the bottling process down, but it can actually be pretty fun. I really enjoy bottling, I try to remember I got into this hobby because I enjoy making my own beer and bottling is part of that. I have a nice kegging system but I still bottle a lot for the enjoyment.
Best of luck!