Oh cool, once I get my ledger wallet, will open a LBC account. Thanks.
on LBC, I can't find any seller taking bank transfer. I definitely not sending cash by mail or starbucks card. Does that means I am left with Coinbase with high fee, where they support bank transfer. Yeah I understand that means I am not anonymous.
When you buy on localbitcoins using their escrow system (and you should), then the bitcoins are immediately deposited in your localbitcoins account. The transaction does not go through the block chain. It is managed completely by LBC's accounting system. You can withdraw them to your own wallet at your convenience.
As long as they stay within the escrow system, buyers are very well protected. Buyers run into problems when scammers convince them to go outside the system.