Template is only the visble part of joomla .  Boostrap is css selector ( id class) that are use inside specific html structure hiearchy even if new concept like SMACCS OCSS try to use the same "xpath selector" to different  html tag structure  !!  .
For focus on the answer
1. You use a template which is already compatible with bootstrap ( template that override which extension  ?  )
2. You use a template which isn't, and you also install and configure a boostrap compatibility plugin ( which plug in ? some name ?)
----vaporware  = no extension name  or too limited number of extension (CMPLT ,component ,Modules ,Plug in ,Language, Template )
----Is there a documented template that  list all the extension name that have been implemented/override  using  boostrap  ?
----joomla is by default free, Is  there a free mature efficient boostrap ( layout view) port with some parameters on back End for joomla today !!
So if joomla or CMS have to support bootstrap  ( in the front side )  then all the joomla CMS Layout view ( for core and extension )   has to implement  this hiearchy  and generate using php the logic for bootstrap . For an example see which selector and html hiearchy is use by default for menu and have a look to how many way bootstrap menu ca nbe implemented in Bootstrap framework . Menu must take care of  which item is active , the  level of the item is active or mouse hover and it the item contain link or not  amoung others  rules specific to joomla ( alias, iln18, right ) .
Go from Joomla 1.5 to  joomla 2.5  was a nightmare because  of incompatibilities  and boostrap 2.X is incomptatible with bootstrap 3.x . so ......It ll take time to see boostrap 3 implemented in joomla  core and extension (joomla 4 ?)   ! .
I am not an advanced user  so my questions  are ?
1) Is  there a joomla version that support for all html view the boostrap logic ( core level and all default extension bundle with joomla )   which version ( joomla , bootstrap,  framework if one is use ? ) Is it free  ?
2) If  logic is implemented in the server side in php, is there a way to find if bootstrap css framework is implemented by the extension ? in the JED the search form have no option to select know if extension use boostrap !!!
3) if joomla support bootstrap it is for be able to support the giant javascript library, theme tool , editor available /  implemented for bootstrap !! So  we see bootstrap plug in/component  ( default or third external ) as a way to avoid the use of some joomla extension ( style gui extension ) ?
Regard's
Menu extension in joomla in  
	jed 
Menu in 
	boostrap
 ( nav bar , button group )
Menu for 
	boostrap
 implemented by non  official boostrap team  ( Ctr F  menu)
Joostrap seem the only  mature way to use bootstrap  but not efficient  information at this time how it is implemented and there is many pay extension. Joostrap seem also to be a pay product .  We don't know if this product rewrite of ALL the layout view for html output  of all extension bundle by default in joomla ? The information must be available in the website but hide somewhere ?