Timeline Info from Script:
When the Young Prisoner (Young Talia, though not introduced as such at the time) is introduced, the Script says she is 'about 10'.
INSERT CUT: a child of about ten looks up towards the light
When Miranda Tate is introduced, the Script says she is in her 30s.
Alfred talks to an elegant woman, thirties, Miranda Tate.
So the short answer is 20-29 years between Talia Al Ghul escaping the prison and the beginning of the events in The Dark Knight Rises.
Batman Begins Script info:
Bruce Wayne is age 8 in the first scene where he falls into the cave.
This is Bruce Wayne, aged 8
Bruce Wayne is age 28 when he meets Ra's Al Ghul:
BRUCE WAYNE aged 28
Bruce Wayne's 30th Birthday is at the end of Batman Begins:
EARLE: Not yet. I checked the trust, and Bruce can’t assume control until his thirtieth birthday. (presses intercom) Jessica, where’s that coffee?
BOARD MEMBER: But that’s in three months.
Timeline Info from Movies:
In Batman Begins
This was after his wife took his place (with Talia). It's also implied that he had found out he had discovered her fate at this point and gotten his revenge.[source]
Henri Ducard: But I know the rage that drives you. That impossible anger strangling the grief, until the memory of your loved ones is just poison in your veins. And one day you catch yourself wishing the person you loved had never existed, so you'd be spared your pain. I wasn't always here in the mountains. Once I had a wife, my great love. She was taken from me. Like you, I was forced to learn that there are those without decency that must be fought without hesitation, without pity. Your anger gives you great power, but if you let it, it will destroy you, as it almost did me.
Bruce Wayne: What stopped it?
Henri Ducard: Vengeance.
Bruce Wayne spent 7 years traveling abroad according to Alfred in Batman Begins:[source]
Bruce Wayne: Have you told anyone I'm coming back?
Alfred Pennyworth: I just couldn't figure the legal ramifications of bringing you back from the dead.
Bruce Wayne: Dead?
Alfred Pennyworth: You've been gone seven years.
In The Dark Knight,
The Joker: Let's wind the clocks back a year. These cops and lawyers wouldn't dare cross any of you. I mean, what happened? Did... did your balls drop off?
I interpret this as one of two possibilities: 1) a year ago batman didn't exist; or 2) a year ago Bruce Wayne was just starting as Batman and had not yet dealt a crippling blow to their organization.
In The Dark Knight Rises,
John Blake: Those men locked up for eight years in Blackgate, and denied parole under the Dent Act, based on a lie?
So, The Dark Knight Rises takes place at least 9 years after Batman Begins.
So, from all of this:
Between 20 and 29 years passed from the time Talia escaped to the events at the beginning of The Dark Knight Rises.
Bane in the prison is at least in his late teens. All we see of him is a fairly young looking face.
So, we have a rough timeline. Assume year 0 is Bruce Wayne's birth. Years in italics, the specific year is unknown and provided as ranges which should contain all possible years, Years in bold are certain, and based on above sources. Any range (i.e. 0-9) indicates the exact point at which the event occurred is unknown, but could be anywhere in between, based on above sources.
0: Bruce Wayne Born.
0-9: Talia Al Ghul born.
10-19: Talia Al Ghul is about 10, escapes the prison, Bane is at least in his late teens, early 20s.
10-28: Talia Al Ghul finds her father, rescues Bane from prison. They are trained by the League of Shadows. Bane excommunicated.
22: Bruce Wayne leaves Gotham, travels the world living amongst criminals.
28: Bruce Wayne meets "Henri Ducard"(Ra's Al Ghul) and trains under him.
29&30: Bruce Wayne returns to Gotham, events of Batman Begins, Ra's Al Ghul's death.
30-31: Events of The Dark Knight
38-39: Events of The Dark Knight Rises. Bane is at least about the same age as Bruce Wayne.
So, based on that, there does seem to be an age problem. I don't think it was ever explicitly stated that Bane is younger than Bruce Wayne, just that Bruce Wayne was no longer in his top physical capability, being a recluse for 8 years and using a cane.
Timeline Info from Actors/Actresses age:
This doesn't really give a definitive age for any of the characters, especially Bruce Wayne and Bane, but it's extra information I looked at before finding the above, so I included it here. Ages are rough, due to assuming the actor/actress had their birthday for 2011 at the time of filming. 2011 was chosen as an estimate of when filming took place, since the movie came out in Summer 2012, leaving time for post-production.
The actress who played Young Talia is Joey King, was 12 in 2011. The character appears to be anywhere from 8-13.
The actress who played Adult Talia/"Miranda Tate" is Marion Cotillard, was 36 in 2011. The character appears to be anywhere from late 20s to mid 30s.
The actor who played Bane is Tom Hardy, was 34 in 2011.
The actor who played Bruce Wayne/Batman is Christian Bale, was 37 in 2011.