Use iTunes to convert AIFF to mp3.
I do this all the time.
iTunes (menu) > Prerences… > Importing > “Import Using:” > MP3 Encoder “Setting:” > (choose “High” or “Higher” for best quality) > “OK” (closes preferences).
Drop your AIFF clip into an iTunes open window, click once on your clip to select it, and choose:
Advanced (menu) > Convert Selection to MP3.
Works VERY fast and stores new MP3 file in the iTunes library.
You can do a “search” (apple f) to locate the new MP3 file on the hard drive and then just drop it into an email.