I am a UK Citizen living in Bermuda. Does anyone know how to apply for a visa to China from Bermuda?

Shelly, if you want to apply for a tourist L type, you should first prepare the required documents including your passport and its copy, the completed application form, a passport-style photo, hotel booking record and two-way air tickets.
And then submit the application to the CVASC in UK to apply for it or post your application there for the application.