Bridge announced he did not wish to be picked for international duty, stating that his position in the squad could be "untenable and potentially divisive" following allegations that his ex-girlfriend had an affair with Chelsea and England defender John Terry.
United's squad has been depleted because of injuries, players away on international duty and Rio Ferdinand still serving a suspension for missing a drugs test.
Mitchell first came to the Welsh public's attention when plucked from being a Neath regular in the Principality Premiership to be a member of the national squad's 2009 tour to north America, while Jones was on British and Irish Lions duty in South Africa.