Unusual Session Errors

Out of nowhere my install using the latest CMSB version has suddenly, without making any changes, started to see session errors fill up the dev log files. Nearly all of these seem to be created when Microsoft's bingbot tries to crawl one of the CMS pages, including 404 pages under the CMSB dir and ordinary pages that merely output data and don't even use sessions.

The errors tend to follow the patter of this single example and cannot be re-created by a human, at least not by me:

#627 - E_USER_ERROR: Couldn't start session! 'session_start(): Cannot send session cache limiter - headers already sent (output started at /-------/system/lib/errorlog_functions.php:69)'!
/-------/system/lib/init.php (line 713)
https://www.-------.co.uk/isp_list/ISP_Detail_Bundle.php?one-bill-telecom-142

#626 - E_WARNING: session_start(): Cannot send session cache limiter - headers already sent (output started at /-------/system/lib/errorlog_functions.php:69)
/-------/system/lib/init.php (line 713)
https://www.-------.co.uk/isp_list/ISP_Detail_Bundle.php?one-bill-telecom-142

#625 - E_NOTICE: session_start(): ps_files_cleanup_dir: opendir(/tmp/.priv) failed: Permission denied (13)
/-------/system/lib/init.php (line 713)
https://www.-------.co.uk/isp_list/ISP_Detail_Bundle.php?one-bill-telecom-142

I've already raised this with Robin as part of a CMSB development project that it is affecting too but I wondered if anybody else had seen the same over the past few days?

I note under 'General Settings' that CMSB has two fields that are both blank at present, session.save_path and session.cookie_domain, should I put something in those? Will that solve it? I've never needed them before.