您可以尝试将"chosenUser"存储到数组中，而不是使用普通的javascript对象表示法.像这样:

You could try to store 'chosenUser' into an array instead of using plain javascript object notation. Something like:

function CalendarController() {
       var vm = this;

       //THIS IS THE VARIABLE I'M TRYING TO PASS TO getDayClass
       vm.chosenUser = ["UserNameWillBeHere"];

       //OPTIONS PASSED TO BOOTSTRAP DATEPICKER
       vm.options = {
            customClass: getDayClass
       };

       //THIS IS THE FUNCTION I RUN FROM HTML WITH NG-CLICK AND IT EXECUTES 
       //FUNCTION getDayClass (AMONG OTHER THINGS)
       vm.refresh = function() {
          $("#calendar").data("$uibDatepickerController").refreshView();
       }

       function getDayClass(data) {
           var date = data.date,
           mode = data.mode;

          //RETURNS UNDEFINED (ONLY INSIDE THIS FUNCTION) 
          //EVEN AFTER USER HAS BEEN CHOSEN
          console.log(vm.chosenUser[0]);
           ...
       };
    }