Bebb was born in Butler County, Ohio to Welsh immigrants. After finishing, he taught school while studying for the bar. He began practicing law in 1831. A devoted campaigner for William Henry Harrison in 1840 and for Henry Clay four years later, Bebb was nominated by the Whigs in 1846 for the governorship. Bebb served a single term beginning in December1846. His term technically expired in December 1848, but was extended into January1849 due to a number of close statewide elections which necessitated delaying the inauguration of a successor. Bebb later moved to Rockford, Illinois.
Ohio's nineteenth governor was WilliamBebb of Butler County, the third native Ohioan to be elected to the office.
William, the first of their three children, who was born on December 8, 1802, is said to have been the first white child born in Butler County west of the Great Miami river.
Governor bebb's term expired in December 1848, but his administration was continued until January 22, 1849, because of a delay in organizing the two houses of the assembly and in qualifying his successor.