The London-headquarted group has taken delivery of the machine at its new mailing, digital print and response handling operation in Cambuslang Business Park, Glasgow.
Peter Calderbank, chief executive at Bss, said the Xerox investment would strengthen its print offering while offering "innovative technology".
He said: "With more than 35 years of experience in the sector, we know that our clients are continually looking for ways to reduce printing, storage and management costs, while working to improve their environmental performance.
"We were attracted by the innovative technology of the Xerox Colour 1000 Press and it has helped to strengthen the new mailing, digital print and response handling operation we have recently launched in Glasgow."
The Xerox printer is producing a range of jobs that include bespoke booklets and mailing pieces using its XMPie personalisation software.
Martin Boyle, sales operations manager for Scotland and Ireland at Xerox UK, added: "At Bss, the press has helped expand the organisation’s offerings, increase efficiency and lower running costs enabling them to focus on helping their customers improve the quality of lives and communities."