You can try the following Elisp code. It handles fill-paragraph but not bibtex-fill-entry.
(defun my-bibtex-fill-field (&optional justify)
"Like \\[fill-paragraph], but fill current BibTeX field.
If optional prefix JUSTIFY is non-nil justify as well.
In BibTeX mode this function is bound to `fill-paragraph-function'."
(let ((pnt ...