Managers were brought in to try to keep open the flagship city centre office in St Vincent Street as strike leaders with the Communications Workers Union held their 12th stoppage this year.
The post office want to generate multi-million pound savings by tempting franchisees to run 70 main Crown offices across Britain.
The latest hitlist includes the main post offices in East Kilbride and Cumbernauld with a combined workforce of more than 20.
The Post Office wants to privatise the Cumbernauld site by April, 2015.
But management hope to find a franchisee for the East Kilbride operation before next spring
MP Michael McCann is demanding the Westminster Government abandons the privatisation of Crown Post Offices.
He said: "We all have to decide whether we want a public service with the ability to provide a range of transactions for all groups in society at the heart of our town or a fag-end operation working out of the backroom of another store goodness knows where."
The East Kilbride workers are among more than 110 union members who had been expected to join today's strike.
Ms Bowmaker said: "This is our 12th strike day since Easter Saturday on March 30 and we are as strong now as we were then.
"We are fighting to protect jobs and to protect services.
"Privatisation means fewer workers and that means few services for the public.
"We apologise to customers but we have had no option but to take strike action."