Really sorry to hear of your experiences at Bologne airport. Flying long-haul with a connection is a stressful enough without having further issues to deal with.
But I wonder how many actual BA staff there are at Bologne ?
The reason I ask is because at regional Italian airports the ground handling may be carried out not by the airline but by a ground handling agent.
Sometimes an airline will have limited influence over service standards. It might only have one or two of its own staff posted at the airport or it may have none at all.
This firm claims to handle BA flights along with many other carriers.
The fact that you mentioned a “General Tix Counter” which “serves many airlines” would appear to confirm this.