How do i transfer USDT from Eth Mainnet to BSC mainnet?

So i have ETH in my ethereum Mainnet. Whenever is switch over to Binance Smart Chain Mainnet, my ETH doesnt reflect.

I wanted to send my eth from Eth Mainnet to Binance Mainnet but the address is the same. How do i do this?

I have an option to send ETH to Binance, swap ETH for BNB, then send back to wallet. But i was hoping to avoid gas fees.

Another is, I was thinking of swapping to USDT on metamask wallet, then send from Eth Mainnet to BSC Mainnet. Is this possilbe?

Many thanks in advance for all your help!