Catalyzes the glycosylation reaction which converts zeaxanthin to zeaxanthin bis(beta-D-glucoside). The reaction proceeds in two steps with the monoglucoside as an intermediate. all-trans-zeaxanthin + 2 UDP-alpha-D-glucose = 2 H(+) + 2 UDP + zeaxanthin bis(beta-D-glucoside) Carotenoid biosynthesis; zeaxanthin diglucoside biosynthesis. Belongs to the UDP-glycosyltransferase family.