take in mind that metamask is not necessarily ethereum. Metamask is just an extension that lets you to interact with apps, in that case binance bridge lets you to transact in/out from binance smart chain and binance chain 'only'.

Are u sure of what assets are u trying to swap between chains¿¿ from where do u want to swap and whats the destination?

Theoretically everything is here.

https://docs.binance.org/smart-chain/guides/bridge-v2.html

good luck bud.