OK, I was able to figure it out from this answer. Here's what's working:
$.getJSON("https://www.googleapis.com/books/v1/users/115939388709512616120/bookshelves/1004/volumes?key=MYAPIKEY",function(data){
var titles = [];
data.items.forEach(function(e,i){titles.push(e.volumeInfo.title);});
console.log(titles);
var newTitleString = titles.join(', ');
console.log(newTitleString);
});