Actually it is better for bitlucy to shut the website down first if it is true that the devs are still working to make the website back to normal.
This way, the devs will be able to work on it easier as there is no one can access the website which may disturb what they are working for.
Indeed shutting the website down may make users worry and think bad about it but I think it can be minimized as long as the admin keep in touch with users through support and keep informing the updates regularly.
I agree. From a technical perspective this isn't an unreasonable approach. However, shutting down is an extreme option and may give the impression that the site is no longer operating. A commonly used strategy in these situations is to limit visitors to the website and to post a temporary "we'll be back soon" message. The theory is that the "disappearance" of the site itself creates confusion and anxiety that the site is no longer there and therefore encourages potential users to give up and leave.