First of all, you should not hard-code the 'mdl_' prefix into your SQL queries, as that could be different on different sites (and is always different if you run PHPUnit or Behat tests against your site) - as per the documentation at https://docs.moodle.org/dev/Data_manipulation_API#Table_prefix please use the {tablename} format instead:
$sql = "SELECT bbb.name, ue.name AS UeName, bbb.timecreated, bbb.timemodified
FROM {bigbluebuttonbn} bbb
JOIN {block_report_bbb_user_events} ue ON ue.meeting_id = bbb.id";
Once that is fixed, you can then use:
$DB->get_records_sql($sql);
(note the 's' on records) to get the results.
Be aware, that get_records_sql() will return an array indexed by the first field returned, so if your query produces more than one result with the same 'bbb.name', then you will not see those results (and get a debugging warning, if you have debugging on, which you should when doing development).
You will probably need to add something unique as the first field returned (e.g. "SELECT ue.id, bbb.name, ...")