There is no build-in feature to count/filter linked work item's count of a specific work item type.
As a workaround, you could export tfs query results to Excel and manage the results in excel side. With the help of excel, you should be able to filter out those work items you needs.
Another way is using TFS API to get the work items and their linked work items with bug type, finally count the number of linked work items. About how to use API, please take a look at this related question: Retrieving work items and their linked work items in a single query using the TFS APIs