Bruce added that Bramble's performance in Monday's defeat to Norwich was poor and that he shouldn't have been out clubbing so soon.
He said: "There's a police investigation going on into Titus and obviously I'm restricted in what I can say, but for me, the big disappointment is he shouldn't have been there in the first place.
"With the rewards footballers get, they have a responsibility, a moral responsibility, and I don't think footballers should be in nightclubs on a Monday, Tuesday, Wednesday, especially after you have just been beaten - and how badly he had performed against Norwich as well.
"If it was me, I would be locking myself away for 24, 48 hours and burying my head and making sure when training comes around, that I'm going to go and perform better than I did on Monday night."
Sunderland, who have won only one league game this season and currently sit 14th in the table, host struggling West Brom on Saturday.