Bards have Jack of All Trades and, usually, a high Dex score. That ensures some reliable pickpockets.
If you get the Gloves of Thievery from the Zhentarim trader underground, that'll give you an extra die to roll on Sleight of Hand checks which will make things even easier.
That all being said, Rogues will inevitably be the better class for Sleight of Hand checks lategame.
By the time Rogue reaches level 10, you get Reliable Talent which the ensures Rogues can't roll anything lower than a 10 for some skill checks. This pretty much breaks Pickpocketing, lockpickimg, and trap disarmament.