Convert general regex to bash proof regex

I have the following regex that checks for a password policy. it is validated to work:

(^([zZ]\d{3})*$)|((?=.{9,})(?=.*?[^\w\s])(?=.*?[0-9])(?=.*?[A-Z]).*?[a-z].*)

I want to use the regex in a bash script to validate a psssword the following way :

echo $password | grep "(^([zZ]\d{3})*$)|((?=.{9,})(?=.*?[^\w\s])(?=.*?[0-9])(?=.*?[A-Z]).*?[a-z].*)"
 if [[ $? -eq 0 ]] ; then
 

This does not work in bash.
My question is :

How do i convert this "pure" regex to a one that work in bash ? which characters do i need to escape, what is the correct way to pass the regex to grep ? are there any other things i need to look out for ?

Thanks

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