In January 2016, Bingham travelled across South America from west coast to east coast by bike. Sir Ranulph Fiennes commented that 'Laura is a very brave person, this is a risky undertaking.With only the equipment she could carry with her, she cycled 7,000 km over 164 days, from Manta on the Pacific coast of Ecuador, through Peru, Bolivia and Paraguay, to arrive at her final destination in Buenos Aires, on Argentina's Atlantic coast, on 1 July 2016. Bingham journeyed across South America with no money, relying on human kindness and generosity, whilst raising awareness for the UK based charity Operation South America.
In April 2018, Bingham conceived, organised and led the first-ever descent of the Essequibo River in Guyana. Contrary to the expedition's own knowledge, when they arrived in the Wai Wai village to begin their journey the Wai Wai told them that they would be the first people ever to visit the source of the river. A German-Guyanese expedition had claimed the feat but the Wai Wai explained that that expedition had run out of time and "faked" reaching the source. As a result, Bingham, alongside expedition members Pip Stewart and Ness Knight and their Wai Wai guides, became the first ever team to visit the source and then paddle the entire river to the Atlantic Ocean.
