Here is how you can unlock additional Basses in Co-Op mode:

Gibson SG Bass - Beat 10 Songs

Gibson Grabber - Beat 20 Songs

Gibson Thunderbird - Beat 30 Songs

Gibson Les Paul and skin - Beat 40 Songs

Hofner Bass - Beat every song

Lava Pearl Musicman Stingray - Get 5 stars on at least 10 songs

Cream SG - Get 5 stars on 20 songs

Natural Sunburst Gibson Thunderbird Bass - Get 5 stars on every co-op mode song (stacks with below)

Natural Maple Gibson Grabber Bass - Get 4 stars on all co-op mode songs