To be honest, I think you are really overthinking this. Using a phone as a player does work well, but I personally prefer something a little less fragile when biking; after all, it might fall out of your pocket or whatever and smash into the ground. Also, battery life on a smart phone isn't the best.
I still think a
simple one like the image below would suit you fine, and is cheap enough not to be a "big deal" if it gets dropped/ruined. And this one even has an FM tuner.
I have one very similar to this and it simply appears as an external drive in Windows when connected, so drag-n-drop works fine. Simple to use, fits easily into a pocket, and just works.
As far as sound quality, it's more in the headphones than anything. As long as the internal amp is even
halfway decent and you don't turn the volume up into clipping, you won't be able to tell the difference between that and a $100,000 player when listening to MP3's on earbuds. Plus, you say that you plan to use only one earpiece when riding, which makes the SQ argument even more moot.
So, just pick a player already!
Rip some songs off your fav CDs, copy them to whatever device, and that's it.