I have been dealing with a thoracic disc bulge doing an Air Squat… of all movements!
If the disc is truly bulging and their aren’t any neurological symptoms accompanying it (unrelenting burning pain or tingling) then at the moment there isn’t any reason to not keep training as long as you avoid terribly painful movements. At this point I would use a softer type ball for any thoracic spine mobilizations, think the balls Jill Miller sells at yogatuneup.com. The important things are maintaining mobility and strength around the injured area. The thoracic spine should be fairly mobile and it will stiffen up with the injury. Face pulls, rows if they are tolerable.