Bash Directory – How to Reference a File’s Directory from the Command Line

The way I used to do this is to create a directory that contains symlinks to the directories you want shortcuts do, and add that directory to your CDPATH. CDPATH controls where cd will search when you switch directories, so if that directory of symlinks is in your CDPATH you can cd to any of the symlinked directories instantly:

mkdir ~/symlinks
ln -s /usr/bin ~/symlinks/b
export CDPATH=~/symlinks
cd b   # Switches to /usr/bin

The downside of course is it won't work if there's a directory in your current directory named "b" -- that takes precedence over the CDPATH

I normally dislike answers that say "first you need to switch shells", but this exact feature exists in ZSH, if you're willing to use that instead; it's called named directories. You export a variable foo, and when you refer to ~foo it resolves to the value of $foo. This is especially convenient because it works in commands besides cd:

echo hi > /tmp/test
export t=/tmp
cat ~t/test   # Outputs "hi"

By issuing the command complete you'll get the list of all completion definitions. Then you can search the offending definition somewhere in /etc/bash_completion and /etc/bash_completion.d. There can be also some .bash_completion in your home directory. On my system the $HOME variable is completed properly, but then fails to complete anything.

Did you try to use ~ instead of $HOME? It's easier to type and it works as expected...