Textbox not clickable in TinyMCE modal box

After looking into what you said about inserting an image, I also found it's the same behavior with videos. And it led me to believe the reason why is because you need to use a file manager plugin in order to handle files in TinyMCE, such as MoxieManager.

Once you have that, your image/video windows will look like this:

Then you will be able to choose and accept files.
Here is the official answer from the TinyMCE FAQ page:

Since you are using Bootstrap (also applies to jQuery UI Dialog), the TinyMCE modal window is losing focus when launched so you can't click inside. The below code will prevent that from happening.

TinyMCE in a jQuery UI dialog

TinyMCE portion of code:

tinymce.init({
    selector: "textarea",
    plugins: [
    "advlist autolink link image lists charmap print preview hr anchor pagebreak",
    "searchreplace visualblocks visualchars code fullscreen insertdatetime media
     nonbreaking",
    "save table contextmenu directionality emoticons paste textcolor"
   ],
   toolbar: "insertfile undo redo | styleselect | bold italic | 
alignleft aligncenter alignright alignjustify | bullist numlist outdent indent | 
link image | print preview media fullpage | forecolor backcolor emoticons", 
   style_formats: [
        {title: 'Bold text', inline: 'b'},
        {title: 'Red text', inline: 'span', styles: {color: '#ff0000'}},
        {title: 'Red header', block: 'h1', styles: {color: '#ff0000'}},
        {title: 'Example 1', inline: 'span', classes: 'example1'},
        {title: 'Example 2', inline: 'span', classes: 'example2'},
        {title: 'Table styles'},
        {title: 'Table row 1', selector: 'tr', classes: 'tablerow1'}
    ]
});

JQuery Modal focus fix:

// prevent Bootstrap from hijacking TinyMCE modal focus    
$(document).on('focusin', function(e) {
  if ($(e.target).closest(".mce-window").length) {
    e.stopImmediatePropagation();
  }
});

JSFiddle

Problem:

If you have a bootstrap modal with TinyMCE inside it and you want to insert a link or other option where it opens a tinyMCE dialog with text input field you cannot get focus on the input text fields (like it is in a disabled state)

Solution:

Remove the tabindex="-1" from the bootstrap modal html. This can be done in on the modal html container or prior initialization of TinyMCE.