For his part, Bruce did nothing to stop Tony. He didn't even call out to him as he left, because he had an inkling of what his friend was going through, and had their roles been reversed, he'd probably want to run, too. If anything, he felt guilty for being the harbinger of bad news.
Would Tony be alright? Bruce trusted him enough not to do anything stupid, like hurt himself, but after a bombshell like this? Nothing was going to be really alright anymore, was it?
His eyes followed Tony out the door, and once he was gone, Bruce hung his head and decided he also needed to be alone, to assimilate what he'd just seen.