ちょっと引用が長くなりますが、手元の辞書(Fairchild's Dictionary of Textiles)に下記の記述がありますので、ご参考に供します。

bobbinet
A machine-made net fabric with hexagonal meshes, made of cotton, silk, rayon, or nylon.

circular loom
A type of progressive shedding loom that produces fabric in tubular form.

tulle
A fine, machine-made net with a hexagonal mesh of silk, cotton, or manufactured fiber. It is softer than maline and is used for millinery and dress trimming or embroidered to form lace. Named for the French city of Tulle. During the 18th century this term was applied to all hexagonal mesh fabrics regardless of where they were made. First made by machinery in Nottingham, England, in 1768. The invention of the bobbinet machine in 1809 further helped the industry and first factory with such machinery was opened in Tulle in 1817. In 1834, the first machine-made figured tulles (point d'esprit) were made, and in 1942 embroidered tulles were produced by applying the jacquard system to the embroidery machine.

fabric in tubular formは、日本語で｢袋織り｣と呼びます。bobbinetは｢ボビネット｣でいいようです。（下に示すURLの『繊維用語辞典』参照)