The bridge is named after Frances Pulteney, wife of William Johnstone. He was a wealthy Scottish lawyer and Member of Parliament. Frances was the third daughter of MP and government official Daniel Pulteney (1684–1731) and first cousin once removed of William Pulteney, 1st Earl of Bath. She inherited the Earl's substantial fortune and estates close to Bath in Somerset after his death in 1764 and that of his younger brother and heir in 1767, and the Johnstones changed their surname to Pulteney. The rural Bathwick estate, which Frances and William inherited in 1767, was across the river from the city and could only be reached by ferry. William made plans to create a new town, which would become a suburb to the historic city of Bath, but first he needed a better river crossing. The work of the Pulteneys is memorialised by Great Pulteney Street in Bathwick, and Henrietta Street and Laura Place, named after their daughter Henrietta Laura Johnstone.
Initial plans for the bridge were drawn up by Thomas Paty, who estimated it would cost £4,569 to build, but that did not include the shops. A second estimate of £2,389 was obtained from local builders John Lowther and Richard Reed; it included two shops at each end of the bridge, but work did not begin before winter weather made construction of the pillars impossible. In 1770 the brothers Robert and James Adam, who were working on designs for the new town at Bathwick, adapted Paty's original design