Are you sure that this is really why your site is heavy? I ask why I consider Bootstrap too light.
As for your question: Yes, is perfectly possible.
This is provided by some frameworks. In the specific case of Bootstrap go to http://getbootstrap.com/customize/ and select only what you want to use. There are other possible customizations as well.
I’ve heard of people deleting unused functions from jQuery source code, but I don’t recommend it because it might break some plugin. In this case there is no automated tool, you would have to do it manually anyway.
But I recommend you not to worry too much about it, because I find it very unlikely that Bootstrap/jQuery will be the performance bottleneck of your site. The most common error is abusing Javascript.
Instead look for tips like the ones below:
Another good tool for testing a site’s performance is the Pagespeed google.
– Kazzkiq