As you surmise the bind offs have to be at the beginning of the row. When you do the other front the bind offs will be on the RS.

When you next feel like learning a new technique there is a way of doing the decreases that avoids the step phenomenon and gives a nice smooth edge.

It’s the Sloped Bind Off here http://www.knittinghelp.com/knitting/basic_techniques/bind-off.php
about half way down the page