.bib library file in a different directory, how to use? (Mendeley centralised .bib file)

You can store your bib file in $LOCALTEXMF/bibtex/bib or any subdirectory of it. Then LaTeX (and BibTeX, biblatex, and biber) will find it. Note that you have to update the filename database whenever you put a new file in this location (but not when the file is only updated). The $LOCALTEXMF part can be any directory which is known to your TeX distribution. For further information about this, see the UK TeX FAQ:

• Which tree to use
• What is the TDS?
• Installing files “where (La)TeX can find them”

Since v1.2, biblatex supports remote location of bibliography resources (i.e. resource from a website); this feature requires Biber as backend (and the use of the \addbibresource command which replaces \bibliography). See section 3.7.1 of the biblatex manual for details (http://mirrors.ctan.org/macros/latex/contrib/biblatex/doc/biblatex.pdf).

Another possibility is to call bibtex with the --include-directory flag. So, instead of,

bibtex myfile.tex

do

bibtex --include-directory="path/to/bibliography/folder" myfile.tex

This is a particularly easy solution if you're using a dedicated editor such as Texmaker, WinEdt, TeXnic Center or emacs with AUCTex. In Texmaker, you can edit the bibtex command used by the editor by going to Options -> Configure Texmaker -> Commands. Directions for the other editors I mentioned are described in this post.