You can exit or otherwise stop execution outside your target interval:
# Get current hours and minutes.
h=$(date +%H) m=$(date +%m)
# If it's less than 9:30, exit
[[ $h -lt 9 || $h -eq 9 && $m -le 30 ]] && exit 1
# If it's after 4, exit
[[ $h -ge 16 ]] && exit 1
yourcommand