Is there a directory history for bash?

Have a look at autojump:

One of the most used shell commands is “cd”. A quick survey among my friends revealed that between 10 and 20% of all commands they type are actually cd commands! Unfortunately, jumping from one part of your system to another with cd requires you to enter almost the full path, which isn’t very practical and requires a lot of keystrokes.

autojump is a faster way to navigate your filesystem. It works by maintaining a database of the directories you use the most from the command line. The jumpstat command shows you the current contents of the database. You need to work a little bit before the database becomes usable. Once your database is reasonably complete, you can “jump” to a commonly "cd"ed directory by typing:
j dirspec

There is

cd -

that is "cd[space][hyphen]" command, which goes to the directory you were before, essentially a "history of depth 1". Repeated "cd -" switches back and forth between two directories.

Quoting man page:

The following operands shall be supported: [...]

When a [hyphen] is used as the operand, this shall be equivalent to the command:

      cd "$OLDPWD" && pwd

Unfortunately, I don't know of a real built-in directory history.

You can build your own cd command with pushd, popd, dirs builtin commands.

Usage

• cd -- ( list current history )

• cd -num ( go to num directory )

• cd - ( go to previous directory )

function cd () 
{ 
    local hnum=16;
    local new_dir index dir cnt;
    if ! [ $# -eq 0 ]; then
        if [[ $# -eq 2 && $1 = "--" ]]; then
            shift;
        else
            if ! { 
                [ $# -eq 1 ] && [[ $1 =~ ^(-[0-9]{,2}|-|--|[^-].*)$ ]]
            }; then
                builtin cd "$@";
                return;
            fi;
        fi;
    fi;
    [ "$1" = "--" ] && { 
        dirs -v;
        return
    };
    new_dir=${1:-$HOME};
    if [[ "$new_dir" =~ ^-[0-9]{,2}$ ]]; then
        index=${new_dir:1};
        if [ -z "$index" ]; then
            new_dir=$OLDPWD;
        else
            new_dir=$(dirs -l +$index) || return;
        fi;
    fi;
    pushd -- "$new_dir" > /dev/null || return;
    popd -n +$hnum &> /dev/null || true;
    new_dir=$PWD cnt=1;
    while dir=$(dirs -l +$cnt 2> /dev/null); do
        if [ "$dir" = "$new_dir" ]; then
            popd -n +$cnt > /dev/null;
            continue;
        fi;
        let cnt++;
    done
}

bash has pushd/popd/dirs. I have this in my .bashrc to auto-push directories onto bash's stack.

#let cd also pushd directories into stack. Use popd to reverse stack
function cd ()
{
  if [ -e $1 ]; then 
    pushd $1 &> /dev/null   #dont display current stack 
  fi
}

Pop these using popd and display the stack using dirs