Bell-bottoms were worn by American sailors during the War of 1812 and were eventually adopted by the British Navy in the 1850's. There is little documentation as to why, but a practical explanation often given is that the navy issue pants, when removed, can be inflated and used as life preservers.
As far as the "expert" opinions are concerned, in the fashion world they are correct. Bell-bottoms first came on the scene in Europe in the mid 1960's and those originals are considered a rare prize by vintage clothing enthusiasts. In 1967, they came to North America and were immediately adopted by the hippie sub-culture. Worn with love beads, granny glasses and tie dyes, they became a signature look for those who embraced free love, peace, and hallucinogenics.
In the 1970's, bell-bottoms entered mainstream society after gaining national attention on the Sonny and Cher show. They sold fairly well in both Europe and America and became part of the disco look in the mid 70's. This proved to be the downfall of bell-bottoms. Disco proved to be a short-lived era in music and by 1979 the popular pants style, along with leisure suits, became a thing of the past to be bought only by those looking for old vintage clothing.
The 1980's saw parachute pants and the 1990's was the time of the Grunge look, but bell-bottoms in their pure form did not come back into style. A less drastic "boot cut" was introduced in Europe in the late 80's and made it to North America within a few years after that. As the years have gone by since, boot cuts have become a mainstay in modern fashion and you can sometimes even see a style that resembles those wide flares of the 1960's. If you're lucky, you'll see them worn with a tie dye or baby doll to complete the retro look.
Chances are, though, the wearer bought the outfit at a vintage clothing site.