Thanks to Howcanoe Wang's nice debugging, I was able to write a script that I place right after the bibbase script to fix things up for Bootstrap 5:

bibbaseHeaderElem = document.getElementById("bibbase_header");
for (dropdownToggleElem of bibbaseHeaderElem.getElementsByClassName("dropdown-toggle")) {
    dropdownToggleElem.setAttribute("data-bs-toggle", "dropdown")
}
for (menuElem of bibbaseHeaderElem.getElementsByClassName("dropdown-menu")) {
    for (aElem of menuElem.getElementsByTagName("a")) {
        aElem.classList.add("dropdown-item");
    }
}

Hopefully bibbase will upgrade to Bootstrap 5, but until then...

Thanks for the help!

Can I suggest that you at least say something like "The remainder of the field name will be used as link description (which will show if enabled with CSS)" in the documentation? That way it's clearer why it doesn't show up by default.

Also, it seems that "theme=default" does indeed display the link descriptions, while leaving the theme off doesn't. The documentation says that "default = "default"" for the theme, but the following two links display differently:

http://bibbase.org/show?bib=http%3A%2F%2Fclulab.cs.arizona.edu%2Fpapers%2Fclulab.bib&theme=default

http://bibbase.org/show?bib=http%3A%2F%2Fclulab.cs.arizona.edu%2Fpapers%2Fclulab.bib

Why is that?