Is there a hook in Bash to find out when the cwd changes?

You would have to use a DEBUG trap or PROMPT_COMMAND.

Examples:

trap chpwd DEBUG        # calls the function before each command

PROMPT_COMMAND=chpwd    # calls the function after each command

Note that the function defined in PROMPT_COMMAND is run before each prompt, though, even empty ones.

A better solution could be defining a custom chpwd hook.

There's not a complete hook system designed in Bash when compared with other modern shells. PROMPT_COMMAND variable is used as a hook function, which is equivalent to precmd hook in ZSH, fish_prompt in Fish. For the time being, ZSH is the only shell I've known that has a chpwd hook builtin.

PROMPT_COMMAND

If set, the value is interpreted as a command to execute before the printing of each primary prompt ($PS1).

https://www.gnu.org/savannah-checkouts/gnu/bash/manual/bash.html#Bash-Variables

chpwd Hook in Bash

A trick is provided to setup a chpwd equivalent hook in Bash based on PROMPT_COMMAND.

# create a PROPMT_COMMAND equivalent to store chpwd functions
typeset -g CHPWD_COMMAND=""

_chpwd_hook() {
  shopt -s nullglob

  local f

  # run commands in CHPWD_COMMAND variable on dir change
  if [[ "$PREVPWD" != "$PWD" ]]; then
    local IFS=$';'
    for f in $CHPWD_COMMAND; do
      "$f"
    done
    unset IFS
  fi
  # refresh last working dir record
  export PREVPWD="$PWD"
}

# add `;` after _chpwd_hook if PROMPT_COMMAND is not empty
PROMPT_COMMAND="_chpwd_hook${PROMPT_COMMAND:+;$PROMPT_COMMAND}"

Usage

# example 1: `ls` list directory once dir is changed
_ls_on_cwd_change() {
  ls
}

# append the command into CHPWD_COMMAND
CHPWD_COMMAND="${CHPWD_COMMAND:+$CHPWD_COMMAND;}_ls_on_cwd_change"

# or just use `ls` directly
CHPWD_COMMAND="${CHPWD_COMMAND:+$CHPWD_COMMAND;}ls"

Source: Create chpwd Equivalent Hook in Bash from my gist.