Luke,
Very sorry for the delay on this!
Your site is loading the bootstrap Javascript files multiple times, and that's what is causing the problem. JFBConnect instructs Joomla 3.x to load it's own copy of Bootstrap, which all extensions really should be using. By using the built-in copy, it ensures compatibility across all extensions since it's then a 'known' copy and there's no duplication.
On your site is the following re-inclusion of the library which is causing the issue:
/website/components/com_osservicesbooking/style/bootstrap/js/bootstrap.min.js
If there's a way to disable that inclusion, it should fix the issue with the modal and hopefully shouldn't cause any problems with the osservicesbooking module.
I hope that helps explain, but if you need more info, just let me know.
Thanks,
Alex