PAD's Young Justice is an AMAZING title, second only to Puckett's Batgirl as far as my favorites go, and Bart is consistently awesome in it. However, a few instances aside, he's mostly comic relief in the book. All of the nuances of the character are better showed off in Bart's incredible solo book. Even so, DEFINITELY check out Young Justice. A new fat trade of it just came out.
If you're only interested in trades, you've sadly only got a few options.
There's this:
http://www.dccomics.com/graphic-nove...-in-the-family which contains most of the first 13 issues of Impulse. They left a few issues out, but you still get to meet Bart, Bart's friends, who are actually a really great supporting cast, especially his best friend Carol, you get to see Bart's relationship with Max, which is one of my all time favorite comic book relationships, and you get to see Bart meet my 3rd favorite member of the Flash Family, Bart's cousin, XS.
Then there's this
http://www.dccomics.com/graphic-nove...ercury-falling which you should ONLY read once you're familiar with Bart, his friends and family, his relationships, and his villains. However, if you go into it with all that, you will LOVE it. I personally think it's second only to Return of Barry Allen as far as 'Flash' stories go.
Despite those being your only real options that focus on Bart's solo, Bart was also involved in the major Flash events of the time, such as Dead Heat and Terminal Velocity, which have been collected in trade, and as such include issues of his book.
Also, AVOID the Geoff Johns TT at all cost! While it wasn't Johns idea to make Bart Kid Flash, he DID completely change Bart's personality to the point of making him a completely different character. Also, AVOID Bart's run as the Flash, as they somehow got his character even MORE wrong there.
Bart ended up dying at the end of that book, BUT, the story in which he came back to life, Legion of 3 Worlds, is the closest we ever got seeing Bart act like himself post-2003. (The Kid Flash Flashpoint mini got him decent, but it wasn't nearly as good.)
So yeah, check out those trades above. I can't actually recommend Legion of 3 Worlds to you because it's one of the few Legion stories that actually IS impossible to understand if you aren't a Legion fan.