With it, Bishop displayed his penchant for absorbing and incorporating stylistic approaches from all around the world into his music, which continued with more rawness on his next two releases, Improvika (2004) and Fingering the Devil (2006), due to each album being entirely improvised.

Bishop returned to more structured compositions with his fourth release, and after the death of Sun City Girls’ percussionist Charles Gocher in 2007, his solo work became his primary focus. Bishop signed with Drag City and released Polytheistic Fragments in the fall of 2007.

In 2008, he contributed the track "Corpuscle," a dark piece with traditional Spanish themes embedded, to Wooden Guitar, a various-artists album that also showcased the acoustic works of Jack Rose, Steffen Basho-Junghans, and Tetuzi Akiyama.

He returned to issuing his own material with The Freak of Araby in 2009, and played on his brother Alan's (Alvarius B.) Blood Operatives of the Barium Sunset in 2011. The solo, LP-only Intermezzo appeared from Ideologic Organ in 2012.

Richard issued a collaborative album, this time with composer and sound sculptor W. David Oliphant, entitled Beyond All Defects on Chodpa Media in 2013. Formerly Extinct, by the power trio Rangda (Bishop, guitarist Ben Chasny, and drummer Chris Corsano), was released by Drag City the same year. He and Alvarius B. released the co-billed If You Don't Like It, Don't! on Important in 2014.

Bishop kicked off 2015 with two albums in two months: Road Stories (Kali) with Bill Orcutt appeared on Unrock in January, and the solo Tangier Sessions was released on Drag City in February. Bishop's penchant for duet recordings was illustrated again on Ivory Tower, a collaborative effort with avant axe slinger Ava Mendoza. It was issued in early 2016 by Unrock. ~ Gregory McIntosh & Thom Jurek