He studied at Ysgol Syr Hugh Owen in Caernarfon, then graduated in 1990 from the University of Wales, Aberystwyth, with a BA in history.

[3] He defected to the Conservatives after failing to gain the party's candidacy for a seat on long-serving incumbent Dafydd Wigley's retirement.

He has joined several delegations of the Conservative Friends of Israel group,[4] including one during the Operation Defensive Shield conflict, when he visited for an Israeli military briefing on the Iron Dome defence system.

[10] In January 2012, after a complaint by a constituent, Bebb raised the issue of the sale of Interest Rate Swap Agreements (IRSAs) in Parliament.

After the debate, Bebb wrote to all MPs who had shown interest, inviting them to join an All Party Parliamentary Group seeking meaningful redress for SMEs affected and pursue this on a cross-party basis.

By March 2015 there were over 100 cross-party MPs on the APPG, chaired by Calum Kerr MP; the group was renamed Fair Business Banking.

[11] On 29 June 2012, the FSA reported evidence that over 90 per cent of the sales had been mis-sales and that substantial damage had resulted to SMEs which had been mis-sold these products.

[12] Viewing the slow progress and poor customer outcomes from the bank-led FSA IRHP Review, Bebb then called and led further back-bench debates on the issue — the last in December 2014, when MPs across the house criticised the poor performance of the Financial Conduct Authority (successor to the FSA) IRHP Review scheme.

[17] Some sections of the media had previously criticised the practice of MPs employing family members, as unfair to other potential candidates.

In 2014, he entered a dispute with an Aberconwy constituent after an exchange on Twitter, leading to media criticism of negative comments he made about Asperger's syndrome.

[23][24][25] In April 2015, argumentative emails between Bebb and his local Conservative Party Association chairman were leaked and reported by the BBC.