This is my kind advise to you learn the bass parts for music you already know, get familar with the instrument (not too hard if you're already a guitar player, the stretching and finger strength will already be there), and then just pick music to learn.
Metallica, Iron Maiden, Megadeth, Judas Priest, Black Sabbath are pretty much metal classics and have a range of basslines ranging from easy to hard as nails.
Most pop-punk bands like Blink, Greenday etc have pretty simple basslines which are great for warmups and helping to improve picking (or fingering) consistancy.
some songs for your practicing
Beginner
Metallica - Enter Sandman
Anthrax - Madhouse
Megadeth - Peace Sells.......... But Who's Buying
Metallica - Master Of Puppets
Megadeth - Symphony of destruction
Megadeth - Go To Hell
Intermediate
Metallica - Orion
Anthrax - Caught in a mosh
Anthrax - Got The Time?
Metallica - My Friend Of Misery
Metallica - For Whom The Bells Tolls
Megadeth - Take No Prisoners
Megadeth - Kick The Chair
Advanced
Metallica - Anethesia (pulling teeth)
Rush - YYZ
Metallica - Battery
Guitar Tabs