蚌埠 is a city in Anhui province - here it's a homophone pun for 绷不 (bēngbù, 'can't keep it together'). 蚌埠住了 sounds like 绷不住了 'can't hold it back anymore', used when you burst out laughing or crying.
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Pure internet slang, extremely casual. Born on Bilibili/Weibo around 2021. Never use in formal writing - treat like English 'I'm dead' or 'I can't even'.
