TeXstudio's build process ('Build & View') by default runs pdfLaTeX but not a bibliography tool, which you need to do separately. There is also a need to change the settings to run Biber rather than BibTeX for creating a bibliography. Thus the steps required are as follows:
In the TeXstudio preferences ('Preferences ...' on the Mac or 'Options -> Configure TeXstudio' on Windows), choose the Build tab and alter the 'Default Bibliography' to 'Biber'. Save and close the preferences.
Run 'Build & View' from the 'Tools' menu (or press the two green arrows icon), which will create a PDF but with the bibliography not completed
Run 'Bibliography' from the 'Tools' menu.
Run 'Build & View' again: the bibliography will appear in the PDF.
As noted in comments, it is possible to set up TeXstudio in alternative ways to achieve the same effect. The key is that you have to ensure that the is a sequence
which can be done 'by hand' (as I have) or can be automated in various ways. Note that the same general idea applies whatever editor is used: this is a feature of LaTeX and not of the editor.
On the question of file paths (a separate issue), it is best not to include a path at all but to place the file where it will be 'found': in the current difrectory or somewhere that TeX searches automatically. That is a separate issue, so I'm assuming a demo file reading:
which 'rolls up' the BibTeX database into the LaTeX source.
Some tools for generating LaTeX .bst files (bibliographic styles), such as the docstrip utility, have known compatibility issues with the package csquotes. The csquotes package is a robust quotation management tool, with support for multiple languages and advanced quotation elements of interest to those writing formal academic documents. For those writing theses, dissertations, or other formal documents where a robust quotation management package is required, it is an excellent choice.
One problem with many .bst files available online is that they attempt to define something called \enquote within the style. When used without csquotes, this is fine, but csquotes has its own defined variable called \enquote. LaTeX does not appreciate having two variables with the same name, so it will call an error, and the document will refuse to compile.
The error will look like this:
And it is resolved by redefining one of these variables. I recommend redefining the one in the .bst file to something like \enquotebst. This can be done very easily to your .bst file using find/replace. The risk of modifying csquotes is that you are tampering with a built-in package that might be updated and reset every time TeX updates are downloaded. For example, in the ajs.bst file commonly found online for sociologists, the \enquote variable appears in two places:
Replace "enquote" with "enquoteFILENAME" or "enquotebst" wherever it appears in the .bst file. The error will stop if \enquote was your problem. If the error continues, ensure that your .bst file is in the correct directory and that you are only calling the bibliography once.