drewfx1
Internally MP3's don't really have "bit depth" in the sense of uncompressed audio. The MP3 codec will work using floating point, so there's nothing really to dither to.
"Exactly what happens" is a rather complicated and very technical process. 
Thanks.
What I forgot to mention is, I do export my projects at 44.1kHz/16bit (with dithering) if I need to burn to CD, which honestly, I do less and less of all the time.
What I normally do is export at whatever my project settings are, and make an MP3 directly from that .wav. It's usually a 96kHz/32bit .wav converted directly to a 320k MP3 using Sound Forge.
What I see a lot of people do is, they'll take a *insert khz of your choice here*/24bit project, export/convert it with dithering to 44.1kHz/16bit, then convert it to an MP3. My way of thinking on this is, the less alteration of the original project export you do, the better the end result will be.