After looking at another answer it would seem I need to also pass id field with every call, otherwise it will disable the input.

Sample code that fixed it:

$('.select2').select2({
  placeholder: "Policy Name",
  minimumInputLength: 3,
  multiple: false,
  quietMillis: 100,
  id: function(bond){ return bond._id; },
  ajax: {
    url: "http://localhost:3000/search",
    dataType: 'json',
    type: 'POST',
    data: function(term, page) {
      return {
        search: term,
        page: page || 1
      }
    },
    results: function(bond, page) {
      return {results: bond.results, more: (bond.results && bond.results.length == 10 ? true: false)}
    }
  },
  formatResult: formatResult,
  formatSelection: formatSelection,
  initSelection: initSelection
})

Edit

Since this keeps getting upvoted I’ll elaborate a bit. The .select2() method expects a unique id field on all results. Thankfully, there’s a workaround. The id option accepts a function like this:

function( <INDIVIDUAL_RESULT> ) {
  // Expects you to return a unique identifier.
  // Ideally this should be from the results of the $.ajax() call. 
}

Since my unique identifier was <RESULT>._id, I simply return <RESULT>._id;