Either KI doesn't have a Trials mode like SF4, or I can't find it. Except for the Jago Dojo, what are good ways to learn BnBs with other characters?

There are some trial combos in the Dojo, but those aren't typically combos you use in real matches (just like most trials in SF4).
It's hard to think about combos in KI as traditional "BnBs", because most characters do combos in the same way. You start with an opener, which is usually just a grounded special move, and then you do a mixture of normals (auto-doubles) and linkers (special moves) in a combo until you get broken or you choose to end it. This flow can be followed by every character and there aren't very many specific cases you need to learn (Sadira has some air stuff you can do, some characters will use their "combo trait" to vary this path a bit, but it's not a big departure). If you want more details on how combos work, check out http://ki.infil.net/combo.html
The real trick in learning characters is learning the neutral game, and which safe-on-block openers you should be looking to land. Once you land that, you can perform similar combos between each character in the roster and have success. You don't need to learn too many "character specific BnBs", since they all follow the opener, double/linker, ender path.

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