Why doesn't Bane just detonate the bomb?

He explains this best when he first imprisons Bruce as an homage to the prison where he came from.

He explains to Bruce that he wants him to watch the city struggle on while being held under Bane's martial law. Suffering, hoping that Batman will come to save them or anyone, for that matter.

All the while, he imagines Bruce just laying in his prison, suffering from his injury, watching the city die, until it finally exploded from the core, decimating Bruce's soul. At this point, Bane plans on having Bruce killed, knowing he failed 12 million people all while he just lay in a prison cell, not being able to do anything to stop it.

Of course, as we learn towards the end of the movie, the whole point of the bomb is actually Talia's doing, in order to make Bruce suffer and garner her vengeance for the murder of her father.

He doesn't detonate the bomb for two reasons. First, Bane explains that true torture comes from hope. This is the function of the hole they can climb to try to escape in the prison. When there is no hope, total despair overcomes people and nothing more can torture them when they have given up completely. If there is a perpetual reminder of escape, then hope keeps people suffering. Bane wanted to truly torture Gotham, with the hope that they might survive. Second, Bane wanted to punish Bruce for betraying Ra's and the League by making him watch Gotham's suffering. This was to break Bruce by showing him how he failed the entire city he betrayed the League for.

Bane has a dim view of humanity, especially the people of Gotham. He thinks people, under significant stress and hardship, will turn into maggots, not dissimilar to the way the Joker felt. He wants to screw with their minds. His 'revolution' is a way for him to exploit anti-authoritarian sentiment amongst the people : he positions himself as a liberator, as someone who's on the side of the weak, those who've been crushed by the 'system' - the poor, people who don't like the police.

Put simply : he enjoys watching people squirm, because he and Talia are sadistic bastards whose childhood pain has distorted their view of humanity so much that they cannot see the world as anything but a cruel place. They want to accomplish the opposite of what Wayne does : just like the Joker, they want to encourage people to 'eat each other' ... 'to stay in the sun'.

Why did they leave it so long? They thought they couldn't fail. They were arrogant and reckless, but more importantly : they had a mole inside the 'resistance' who was able to forecast every single move Gordon, Blake et al would make - the mole, of course, being Talia. And one more for one more reason that is obvious but not always apparent : they are fuc*ing crazy. They're not factoring in self-preservation or anything logical : they're trying to create hell on Earth - and enjoying it.

Talia/Miranda Tate wouldn't have destroyed Gotham City when she infiltrated Wayne Enterprises between The Dark Knight and The Dark Knight Rises, since Bruce Wayne supposedly rid Gotham of criminal control. As Miranda Tate she invested in Bruce's clean energy project but he enraged her by mothballing it 5 years in. Bane set up his lair beneath Applied Sciences and recruited people from the lower class of Gotham City to his army, they ran a Coup in West Africa, and crashed the plane in the beginning so Bane can retrieve Dr.Pavel.

Since Bruce refused to use the reactor (understandably), and Bane found Gordon's letter discovering the truth about the Dent Act; they decided to exploit it to torture Gotham City and Bruce Wayne.

Source-The Dark Knight Rises IMDB FAQ