Having been brought up in Pottstown, an industrial community in the state of Pennsylvania, Anne enrolled in the School of Industrial Art of the Pennsylvania Museum. Her studies in America culminated in several years undertaking life-drawing and sculpture at the Pennsylvania Academy of Fine Arts.

Anne was commission to go Paris in 1905 to illustrate the latest up and coming fashions for the periodical, North American. In 1907 on the Paris-Plage, a resort based in the environs of Paris, she became friendly with the painter, John Fergusson. From 1910, Rice was often exhibiting in established galleries both in the UK and France, alongside the Scottish Colourists such as Fergusson and Peploe.

In 1913, she married the English art and theatre critic Raymond Drey who had been previously based in Paris. In addition to her interest in still life painting, the union with her husband bred an interest for Anne in the world of theatre - often the sets and costumes of various productions became the subjects of her work.