Get new bootstrap-VERSION and drop in bootstrap/static.
Manually grep and replace instances of jQuery with (window.$jqTheme || window.jQuery) in files in the new bootstrap-VERSION/js directory.
Update VERSION in sphinx_bootstrap_theme/bootstrap/layout.html
Update bootswatch:
# Create tarball of everything for bootswatch to drop in and replace.
$ cd scm/vendor/bootswatch
$ git checkout v3.3.6+1
$ find . -name "bootstrap.min.css" | \
(echo "./fonts" && egrep -v "\/2|bower_components\/") | \
xargs tar cf - > ~/Desktop/bootswatch-3.3.6.tar