The general understanding in my personal opinion (not refering to any standard):
Open bonnet: any bonnet that will expose /let (leaking) fluid (from stem sealings) or other sources escape to the surroundings.
Closed bonnet: any bonnet that under normal operational conditions will keep the fluid inside the valve or bonnet, even if stem sealings etc. are defect.
A bonnet with a vent hole is then not a closed bonnet, if the vent hole is not properly (permanently?) sealed, and constructed to be sealed under all operational conditions.
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 large areas of the spring are exposed and process fluid will leak to atmosphere through the bonnet. The bellows will prevent this in normal service.
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.
