There are several possibilities, but what works for you depends on the desired format of the text file. You say you want no formatting, but I doubt you would be happy with just the format you get in the .bib file.
From biblatex/BibTeX directly If you use biblatex there is no easy way to obtain the text of the bibliography as it is printed by \printbibliography. (See also Is it possible to mimic the compiled bibliography automatically?).
But if you use BibTeX the .bbl file contains the bibliography with a bit of formatting and LaTeX commands. It is not impossible to change the .bst file that produced this output to only give plain text, but it does take some work. An example can be found in https://gist.github.com/moewew/50795d6f171269e949d71d8c4149468e. You would change your document to use the new bibliography style plain-plain and a compile run would give you a plain-text output in the .bbl file.
biblatex users can try biblatex2bibitem, which combines the copy-and-paste-from-PDF solution with the approach suggested here: Output bibliography as a standard itemized list in bib latex.
Copy and paste from the PDF A simple copy-and-paste job from the PDF (I take it that is what you tried) can be a good one-off solution, but that may require manual intervention to remove possibly unwanted line breaks, page numbers and other oddities. And you may also run into problems with the copied characters not being recognised as intended (you mention "fi" and "ff" ligatures - I have never had a problem with these, but that may well be font- and even viewer-dependent).
Remove LaTeX commands with OpenDetex detex can remove (La)TeX commands and produce a plain-text version of your document. See https://github.com/pkubowicz/opendetex
Convert to document to HTML et al. You could also convert your .tex file to HTML, .odt or another format to obtain an almost-plain-text version of your bibliography. Pandoc and htlatex spring to mind. There are also tools to extract plain text from .dvi or .pdf files, dvi2tty and pdftotext, see https://texfaq.org/FAQ-recovertex.
Convert the .bib to HTML Finally there are tools like bib2html to convert the entries in your .bib file to HTML directly, see also How to quickly convert a single BibTeX reference into a formatted reference?.
Some reference managers like JabRef and Bibdesk also offer a pre-view feature of the .bib entries in certain styles that could be used to produce a plain-text bibliography.
.bibfile and output a.docxor.texrepresentation of what yourbiblatexbibliography would look like in a LaTeX document without the intermediate step converting a TeX document. Of course there ishtlatex/tex4ht... – moewe Jun 09 '18 at 12:32