The ability to add social sharing buttons, and one specifically for BookBub, depends on the type of hosting you have and BookBub itself. If it is something like cPanel, Plesk or WordPress, you should definitely be able to add a button because those require users to customize everything. Some, like WordPress, might even have a plugin you could use.
If you are using something like GoCentral or a Website Builder in general, it can get a little trickier since those don't normally allow outside coding. They do, however, normally allow HTML blocks or links, so it's still possible.
In general, though, it depends on BookBub and if they provide any sort of HTML link. Usually, if a company wants you to add a button to a site, they will give you a code or text and tell you to copy and paste it into your site. If you find something like that, you should be set. A quick look on BookBub's site looks like the might have something like that available in individual profiles, so I recommend checking your account settings or reaching out to BookBub for more details on what they want you to add.