Hi Stefan,
I'm the product manager for BigBlueButton. We recently posted an update of our project here: https://moodle.org/mod/forum/discuss.php?d=337869.
With regards to hosting, as BigBlueButton is open source (like Moodle), you have the ability to install BigBlueButton on a server at your organization and, like Moodle, enjoy all the benefits.
The developers behind BigBlueButton have been working on it for over seven years now (five years on the Moodle integration). They are also working on a mobile client in HTML5 as well. See: http://docs.bigbluebutton.org/html/html5-design.html
If you are using a Moodle hosting provider to host your Moodle, recommend you reach out to them directly -- there are companies that provide hosting for BigBlueButton as well (see http://bigbluebutton.org/support).
Warm regards,... Fred
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BigBlueButton Project Manager