I don't read a lot of YJ/Baby Titans fic, but this is what I remembered off the top of my head. (Also, these were the ones I managed to find links for. There's a lot less DC fic in my bookmarks than I thought.)
These stories are all over the map, timeline-wise. (There's one pre-YJ, some Teen Titans era, one post-OYL.) If anything here confuses you, let me know and I'll try to explain. :)
Not actually Bart-centric, but too hilarious to miss. "I'd make a special bat-proof room so he couldn't escape, and then I'd feed him cake!" Bart announces. The room falls silent. Kon twists to peer at the young speedster. "Why are we keeping him?" Bart asks.
The Case of The Disappearing Felines by jamjar. This story is wonderful. When Bart notices cats going missing in Manchester, he calls Superboy and Robin in on the case. But it's also about Bart's need for friendship and connection.
3) The Great Cheerleading Squad Debacle Of Aught-Three, in which Joan and Jay just didn't have the heart to tell Bart that wearing the same uniform as the girls wasn't the greatest idea.
The author calls this "the Bart/Tim Epic of Woobieness and Nothing Happening".
I cannot categorize this, but you should read it anyway: Mpreurgh by Derry and Propaganda. It's MPreg, like the title suggests, but it's hysterically funny, crackbrained and deeply twisted.