What do you mean by the `default` one? As far as I can see bootstrap.js is only loaded on pages that use tooltips. What do you suggest is the best way to use the bootstrap framework for frontend development, if not loaded in the template index.php?

By the default one I mean !Joomla's bootstrap.js.
You cannot avoid loading it through index.php either way.
This issue rose after version 3.1.5 where the library is loading when necessary.
If someone needs it for his/her frontend he could include the JHtml::_('bootstrap.framework') in order to use the already existing library instead of reloading it through another place.

You could read more about the use of that here:
docs.joomla.org/J3.1:Javascript_Frameworks

Aah I understand now :) Though I'll still use the latest library from bootstrap 3. Your solution makes this possible!

I'll mark this topic as solved then :)