Yes your correct. You need to have Superuser installed.
I recommend two things before you permanently remove your bloatware.
1. If you installed a custom recovery (ClockWorkMod or CWM) on your device when you unlocked and rooted the device, make a Nandroid backup before you start changing things. This way in the event something gets really messed up you can restore the working backup to save your butt.
2. Grab Titanium Backup from the Play Store.
This will do two things by doing #2.
1. Verify upon start up that you indeed have root (Superuser) access installed properly because it will prompt and ask your permission to continue.
2. You can make a backup of any system (Stock Email, Browser, etc.) or non system (3rd party or bloatware) apps on your device so you have them to restore if need be at a later date.
Next grab ES File Explorer from the Play Store. Highly recommended for root and non root file management.
Once you have ES File Explorer running you will need to go into the Settings and scroll down near the very bottom of the settings menu and you will see your ROOT ACCESS options. You will need to mount system and the other options to access and delete/rename/copy/paste apps or (apk's) as they are known to /system/ level access the device.
From there you can navigate to the root level "/system/apps/" of the device and remove whatever apps you feel you don't need any longer. You can also as a safety simply rename the app's to example "Browser.apk" to "Browser.apk.bak" and it will keep the file there in case something doesn't react correctly and you need to restore it back to working order. Once you verify things are acting correctly after temporarily renaming the app you can always go back and delete it completely.
Good luck!