I guess it depends - are you trying to root your Droid RAZR HD? Or a Verizon Galaxy S III? If the latter, are you already on 4.1.2?
The easiest method might be to use Odin (on your desktop computer) to flash a pre-rooted stock ROM, but I'll let others chime in - I rooted back when 4.0.4 was current, so I'm not sure if things have changed much with Jelly Bean.
Out of curiosity, why is the bloatware bothering you so much? For the most part, you can either disable it (so that it doesn't run in the background) or hide it in the apps list so that you never even see it.
What kind of "root apps" were you thinking about downloading? What kind of problem are you trying to solve?
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