You may want to explain what do you exactly mean by "...access visibility grip property...". Do you mean the Visibility defined with the block definition, or the DynamicBlockReferenceProperty in a block reference, identified by its property name, be it a Visibility property, or other type of properties?
If you want to get to the properties defined with a block definition, then you cannot: there is no API exposed to define/change the dynamic properties, and they are not some kind of Entity/DBObject that you can loop through a BlockTableRecord to reach them.
If you want to read/change the dynamic property in a BlockReference, you loop through BlockRedernce.DynamicBlockReferencePropertyCollection and identify the one in interest by its property name.