bag, sack, case, pocket, pouch
帒 centers on a flexible container for carrying or storing items: a bag, sack, case, pocket, or pouch.
帒 is a phono-semantic compound combining 巾 (cloth) with 代, which likely contributes the sound. The cloth radical suggests a fabric container.
A cloth (巾) bag with a handle-like top (代) for carrying things: 帒 is a sack or pouch.
For タイ, imagine tying a bag shut with a tight tie: tie -> タイ, and the bag is securely closed.