Export a function with Node JS

Let's look at your code:

module.exports = {
    ...
};

module.exports = function(owner) {
    ...
}

You're assigning two different things to the same property. The second assignment overrides the first one.

---

To do what you're asking, you need to export the function first and then add the properties separately:

module.exports = function(owner) {
    ...
}

module.exports.User = user;
module.exports.Note = note;

This is standard in node

Instead of defining note and user with var, use exports.note and exports.user

 exports.user = bookshelf.Model.extend({
    tableName : 'tblUsers',
    idAttribute : 'email'
 });

 exports.note = bookshelf.Model.extend({
    tableName : 'tblNotes',
    idAttribute : 'noteId'
 });

Then you'll more likely than not have to set your function export to a named function. (or make it a class?)

 exports.MyClass = function(owner) {
   return knex('note').where('public',1).orWhere({ownerName : owner}).select('noteId');
 }

If you're worried about ease of imports, you can assign MyClass to a variable, instead of the whole package

 var MyClass=require('module').MyClass;