It's a remake of the Gibson Non Reverse Thunderbird II.
Mahogany body with set neck (also mahogany) Rosewood fret board.
The pickup is an Artec AlNiCo humbucker with bar magnets.
So far BaCH made two series: in total there's 30 whites, 10 black ones and 10 sonic blues ones
The basses are not available for people who didn't sign in for this project.
I don't know if BaCH has concrete plans to make a third run of a NR-Tbird II. And I don';t know if they're actually planning a NR-Tbird IV.
Perhaps Roman can tell more.
http://www.bachmusik.com/en/p101177/th-1-whI know they are planning to build a Fenderbird.
I have no idea when...