You should be able to access the Express box through the same utility you set it up with originally once you plug the ethernet cable into it. You should not have to go through the whole process again, either.
It sounds like when you set the Express to not show up in other's wireless options, you did not also tell your computer to connect to your network by default. The setting that keeps yours from showing up for other people simply turns off a function that broadcasts your network name (called the "SSID"), so other people don't see it. This is not a real security feature, by the way; setting up WPA with a decent passphrase is exceptionally good security that's easy to do, while hiding your network is like throwing a sheet over an elephant...
So anyway, I'd turn the network name broadcast back on and see how things work for you. If other people see your network (and you've set up WPA on it) it will be their problem. People who might want to look for networks can use software that will find it whether you broadcast its name or not.