Everyone else kind of covered it, but yeah, there was a longer period of time between when he escaped and when he got to Gotham than it seems if you aren't paying attention. Plus, he's Batman. Finding a way to get himself back into Gotham probably isn't that hard for him. Hell, he may even have had plans in place for getting in and out of the city undetected if he ever needed to. As for someone noticing he escaped, there aren't any guards there. You throw people in the hole and they never get out. Maybe they drop them food and water now and again, but that'd be the extent of it. Not to mention Bane had basically dislocated a disc in his spine. He probably didn't figure he was going anywhere after that.

And I've seen other people confused with why they don't detonate the bomb right away but I'm not sure how the movie could have been clearer in that they wanted Bruce to suffer from watching his city fall before it was finally destroyed. Hell, Bane pretty much outright says that's his goal when he leaves Bruce in the prison.