Ассортимент (assortment) is closer to stock, it's like a list of all your goods. Variety is kinda разнообразие. For example, "у нас большое разнообразие товаров" (sounds a bit awkward, though, coz I translated it literally) = We have a big variety of goods.
Also you can use "выбор", for example: "У нас большой выбор товаров" = We have a large selection of goods. It's very common.
"У нас большой ассортимент браслетов" = "У нас большой выбор браслетов", you can use both.