Bebb was born in Wrexham on 9 October 1968 to a family originating from Bangor and Blaenau Ffestiniog. He studied at Ysgol Syr Hugh Owen in Caernarfon, then graduated in 1990 from the University of Wales, Aberystwyth, with a BA in history. He went on to run an economic development consultancy and work as business development director of Innovas Wales. He was also a partner in his wife's bookshop.
