How to render bootstrap dropdown above the object?

This is by default part of what Bootstrap can do. It's in the docs under Button Dropdowns - Dropup menus

<div class="btn-group dropup">

As it's absolutely positioned, you will need to have some space above the button so you can see the drop up menu, so I wouldn't use it at the top of a page.

I've set up a fiddle here for you. If you remove the <br> at the top, you'll see that the menu options are hidden at the top of the output box.