Prevent Access to Website Under Construction

I’m currently setting up a WordPress site locally (this is my first WordPress site). I think it would be more helpful now for me to be testing the site live, rather than locally.

My webhost (BlueHost) provides the ability to password protect folders of a site. Is setting password protection on the ROOT folder of the site the best way to block unauthorized access to the entire site while it’s under construction?

Most importantly, would password protection block access by ALL search engines, bots, etc.? (I don’t want the site indexed/searched till it’s completed.)

Any other tips regarding this objective?

Thanks very much.