Born into a South African family involved in the wine industry, Anthony's father hosted weekly Sunday luncheons as forums for great discussions and wine tasting. By 1978, he had worked in the Bordeaux and Jerez de la Fontera viticultural regions, completed his Bachelor's degree at Stellenbosch University, and his Master's degree at the University of California, Davis. He then assumed the post of assistant winemaker at Beaulieu Vineyard, where he was responsible for many of the George de Latour Private Reserve Cabernet Sauvignons. In 1989, Bell was named general manager of the esteemed wine estate. He successfully defined the Carneros Region as a viticultural appellation and for five years oversaw operations and winemaking for all of the Heublein Fine Wine Group activities in the Napa Valley, including Inglenook-Napa Valley, The Gustave Niebaum Collection, Christian Brothers and Rutherford Estate Cellars. In 1994, along with two partners, he established Rutherford Benchmarks, a portfolio of wine estates that includes Bell Wine Cellars, Quail Ridge Cellars, Monterey Peninsula Winery, Quail Creek Cellars, Moonshine Vineyard, Fox Creek Winery and Maxus Champagne Cellars. He resigned from Rutherford Benchmarks in 2000 to devote his attention exclusively to his own winery.

He has also conducted important clonal research, beginning in 1980. In conjunction with Austin Goheen of the US Department of Agriculture, Bell planted 14 different selections of Cabernet Sauvignon. One of these selections was from an abandoned experimental station at Jackson, California, located in the northern Sacramento River Valley. The intrepid Goheen used an old parcel map to track down the old field station, where he found grape varieties overgrown and wild. He brought back several cutting; remarkably, none suffered from leaf roll virus. One cutting was thought to have been originally imported from Bordeaux by Paul Masson in the 1880s, prior to the outbreak of phylloxera biotype A.

Fourteen cuttings were planted at BV #4 vineyard, and by 1986, after repeated blind tastings a clear consensus had developed that the 'Jackson' clone's lushly textured fruit, finesse and concentration were truly exceptional, becoming the pedestal upon which he created his dream wine, BELL Cabernet Sauvignon, clone 6.

Working with one of BV's growers and a long-time friend, John Baritelle, the two men shared a passion for quality and began to implement the results of Bell's clonal research, striving for the ultimate expression of terroir. They planted several acres in 1987 to the low-yielding Jackson clone and coaxed the vineyard block with a level of care seldom seen. Beginning with the 1991 vintage, small lots of the vineyard-designated Jackson clone Cabernet Sauvignon were produced, leading to the creation of Bell Wine Cellars. In Bell Cabernet Sauvignon, clone 6, Anthony has created a clear reflection of the vineyard, varietal and clone, and a testament to the concept of terroir.

Long before it became fashionable to talk about wine growing, about winemakers crafting wines from the vineyards rather than from the cellar, Anthony was pursuing a philosophy of terroir. The French term encapsulates the factors which play a role in differentiating one vineyard site from another, including climate, soil, clonal selection, etc. "Wine is grown in the vineyard," explains Bell. "We are merely stewards of nature while the wine is in our cellar."