Use PureDevs WP Locker to hide your dev site from general visitors and known bots.

loftocean

Loft Maintenance

A toolkit to help you lock down your site quickly when your site is not ready to go public.

ympervej86

PureDevs

Use PureDevs WP locker To safeguard your entire WordPress site, by using a single password.
Only the visitors who know your password would be able to access your WordPress site.
This plugin is just what you need if you’re setting up a developmental version of your WordPress site or if your website is going through a major revamping and your website is simply off-limit from the general public or the known bots.
After activating the plugin, head over to Settings> PureDevs WP Locker> Set Password to set a site-wide password.
Note: When a user enters a password, their IP is saved both on cookie and in database table as future login credentials.
Optional: 
Form heading: Clarify to visitors the reason for locking your website and provide clear guidance on the next steps to take. 
Button Label: customize the text on your password submission button.

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