You can bounce your song straight to MP3 from Logic. Just check "MP3" under Destination in the Bounce window (File >Bounce...) and choose the desired Bit Rate. You might want to review videos #105-108 of the Logic 101 tutorial for more information :
You can also convert WAV/AIFF files in iTunes. To do this, click on the "Import Settings" button under iTunes > Preferences, choose the MP3 Encoder and use "Custom" to choose the highest MP3 quality settings. Right click (or Control-Click) the song you want to convert and choose "Create MP3 Version".