paper string
緡 centers on a string or cord made from twisted paper, used historically for binding or threading items like coins.
緡 combines 糸 (thread) with 昬, which likely contributes the sound. The character originally referred to a cord for stringing coins.
The left side 糸 is thread, and the right side 昬 looks like a spool or bundle. Imagine twisting paper into a strong string wrapped around a spool: 緡 is that paper string.
For ビン, picture a paper string tied around a bin full of old coins: bin -> ビン, and the string holds the coins together.