Source — Wikipedia, "Susan Bassnett"

Extract

Bassnett (b. 1945) founded the Centre for Translation and Comparative Cultural Studies at the University of Warwick in 1985, becoming Professor of Comparative Literature there in 1992; she taught at Warwick until her retirement in 2016, and the Centre itself closed in 2009.
Her book Translation Studies (Routledge, "New Accents" series; first published 1980, now in a 4th edition, 2013) is described as a foundational, widely used student introduction to the field.
With André Lefevere she co-edited Translation, History and Culture (Pinter, 1990) and later co-wrote Constructing Cultures: Essays on Literary Translation (1998). The page states that Bassnett and Lefevere together "developed the idea... [that] neither the word, nor the text, but the culture becomes the operational 'unit' of translation" — i.e. the programmatic statement of the cultural-turn position.
Constructing Cultures discusses the "shift of emphasis from original to translation... reflected in discussions on the visibility of the translator" — an idea later developed at book length by Lawrence Venuti (see the Venuti source page).

As a tertiary, crowd-edited source, none of the above is independently confirmed against a primary Bassnett text by this project; treat the "operational unit of translation" formulation as Wikipedia's paraphrase of the Bassnett/Lefevere position, not a verified direct quotation from Translation, History and Culture itself.
The page does not, in the excerpt fetched, explicitly use the phrase "cultural turn" or date it to 1990 — that dating comes from the Liu 2010 source page, corroborated by the Wikipedia "Translation studies" source page.