Right, so, twelve hours in an unsettling house with no escape from tedium and the uncomfortable urge to make smoothies and omelets-- Bruce is more than happy to forget that ever happened and go on about his life, but unfortunately he's entirely paranoid and takes the time to sit down and make an incident report in his files underground.
With that out of the way, he leaves to go find Grayson's apartment. (... Which he might have already made note of some other night, that's not the point.) He didn't tell Jack who he had in mind, because he's honestly not sure if Dick will just take the job - he's inclined to believe that he will, but telling somebody to sit down is not the same as assigning them a significant amount of covert op work, and no matter that his relationship is with some other Bruce Wayne, they're veritable strangers, here.
And now he gets to decide, since Dick doesn't seem to be home, if he's going to try to break in or not.