Please take note that our B2B Login Access Management app works to lock the page(s).
The search bar unfortunately is not a page. Thus, we cannot lock the function. Customers can still see the products when they search, however, when they click on the products, a password field/login form/custom message is shown.
If you really do not want to sneak any information about the restricted products, you had better disable the search function. Or, you should install a Search and Filter app that allows choosing what to show on the search box.
Or you can add us as a staff account so that we can look into your theme and see if it is customizable.
Go to Admin > Settings > Account > Create Staff Account. In the email fill in email@example.com and tick these options: Products/Customers/Apps/Themes/Pages/Navigations/Settings.
We promise to be careful while checking your problem. After that, you can remove our access to your page right away.