I think it is plural: from
encyclopedia.com
Bible the Holy Scriptures XIII. — (O)F. — ecclL. biblia, n. pl. taken as fem. sg. — Gr. (tà) biblía ‘(the) books’, pl. of biblíon, orig. dim. of bíblios, būblos papyrus, scroll.
What does that mean, Noun Plural taken as Fem Singular. Is it both singular AND plural? The singular is biblion.
In English "Bible" is singular. That entry is just about the Latin word, not the English one.
What that entry seems to mean is that in ecclesiastical (i.e. church) Latin, "Biblia" is treated as a feminine singular noun (one of many Latin feminine nouns that end in -a), whereas
originally (in the original, Ancient Rome version of Latin), "biblia" was a neuter plural noun. Given the way Latin works, that would mean that originally the singular was probably "biblium" (like
medium -> media: that's a neuter Latin singular -> plural pair). So, in Ancient Rome, "biblium" meant a book and "biblia" meant books.
The Bible was probably called "Biblia" because it was made up of several books (the book of Matthew, the book of Mark... the book of Revelations... etc.). But then the language evolved, people's usage of the word shifted a little bit, and in the Latin spoken in the church, it started getting treated like a feminine singular noun.