How can I grep complex strings in variables?

if echo "$long_str" | grep -q "$shrt_str";then
  echo "found"
fi

or

echo "$long_str" | grep  -q  "$shrt_str"  && echo "found" || echo "not found"

But since you are using bash shell, then use shell internals. No need to call external commands

shrt_str="guide"
case "$long_str" in 
   *"$shrt_str"* ) echo "Found";;
   * ) echo "Not found";;
esac