I don't currently have full internet access, but Spirax Sarco publish some very informative safety valve information and terminology descriptions on their website and are well worth a look.
In the event of a bellows failure, process fluid will escape from the bonnet vent port. From the above descriptions, this then classes it as an open bonnet. If, however, you stick to safety valve terminology, then a bellows valve is closed bonnet. With respect to safety valves, open bonnet means...