This is a list with Bootstrap 3 templates and companies that provide themes for Joomla. These resources could be useful for you when you would like to create website based on Joomla and Twitter Bootstrap 3.
Developers of Joomla templates
This is a list with companies that develop Joomla templates. Some of them provides frameworks used as core component in their development. In many cases, you have to install the frameworks if you would like to use their templates.
JoomlArt is a leader in development of Joomla themes. You have to install their T3 framework as a plug-in. That is the core of their themes. You can start with one of their free templates T3 B3 Blank.
JoomlaBamboo is another company that provides wonderful themes.
ZooTemplate is part of CleverSoft. It is innovative young companies in the field of Website Design & Development. You have to install their Zo2 Framework and you can start with their free Zo2 Hallo Blank Template.
Joostrap is a company where you can find good Bootstrap 3 templates.
PCMShaper is a website built and improved in Chennai, India. The website is owned by PCMShaper. Their mission is to supply Joomla templates and extensions.
Free Joomla! templates
This is a list with templates based on Twitter Bootstrap 3.
Purity III - developed by JoomlArt
Helix 3 - developed by JoomShaper
Baseline - developed by You Joomla
Eximium - developed by YouJoomla
ZT F7 - developed by ZooTemplate
ZT Marco - developed by ZooTemplate
ZT Shield - developed by ZooTemplate
ZO2 Framework and Zo2 Hallo Blank Template - developed by ZooTemplate
Websites where you can find more Joomla! templates
This is a list of websites where you can look for Joomla! templates based on Bootstrap 3.
I hope, these resources to be useful for you. If you find other templates, you can send information about them via the contact form. I will be happy to include them in the list.