Back-row forward Bradbury has been brought in for the autumn series along with two club-mates – prop Rory Sutherland and uncapped hooker Neil Cochrane.
Ford had been missing for Edinburgh with a calf problem in recent weeks and the Scottish Rugby Union revealed the hooker had withdrawn from the international squad after suffering a chest injury last week.
An SRU statement read: “Ford sustained a pectoral injury in training last week, with a scan at Spire Murrayfield Hospital confirming the injury required corrective surgery at Spire Shawfair Hospital. Ford is expected to be out for around four months and has returned to the care of this club’s medical team.”
Bradbury was left out of the original squad around the time he was stripped of the Edinburgh captaincy months after receiving the honour.
The 22-year-old missed several games last month after suffering a head injury during a night out and Edinburgh head coach Richard Cockerill took action, saying he would not “accept that behaviour from my captain away from the field”.
But the forward – who has two caps – made a try-scoring comeback during Edinburgh’s Guinness PRO14 victory over Ospreys on Saturday to earn himself a recall.
Sutherland, 23, won all of his three caps in 2016 while 33-year-old former Doncaster and Wasps hooker Cochrane comes in after injuries to Ford and Fraser Brown. He will provide back-up to club-mate Stuart McInally and Glasgow’s George Turner.