Sorry, but /usr/bin is still a root/wheel directory, so it is actually going to be worse to install the textwrangler stuff there.
In any case, in your terminal type
echo $PATH and see if /usr/local/bin is in the path. If /usr/local/bin is in your path all the stuff you install there will NOT need root permissions to be run. If it is not, you can add it as such:
go to /etc/paths.d/
create a text file that you can call localstuff (or whatever)
edit localstuff putting /usr/local/bin in it.
$ ls /etc/paths.d/
50-X11 MacGPG2 TeX TeXbin git julia
$ cat /etc/paths.d/julia
$ echo $PATH
make sure that your shell is a login shell in whatever terminal you are using, the OSX predicated way of adding stuff to $PATH seems to break if you do not use a login shell.
As I said though, chances are that /usr/local/bin is in your user's $PATH anyway, so no need to worry. I'd also move all the textwrangler files you put in /usr/bin in /usr/local/bin to avoid future problems.