Your 100% right. As the ative currency you can just send it directly to your account name and not have to worry about using a bridge or gateway (that you see in the deposit/withdraw tab)

To send from polo or bittrex. Just do a withdraw as you would normally but instead of puttinga big complicated address just enter your bitshares username and the amount to send (best to send a few to start with as a test). There is 3 second blocks so you should recieve your bts in you wallet within a couple of minutes (exchanges take a few minutes to process)

Found this guide on steemit in case above is not clear
https://steemit.com/bitshares/@lexikon082/how-to-withdraw-bitshares-from-bittrex-account