Minecraft – ny way to play Bukkit plugins in Single Player without having to make the own server

No. There's an important distinction between Multiplayer mods and Craftbukkit plugins. All SMP mods are automatically compatible with Singleplayer Minecraft and are installed in the same way, but Bukkit plugins are designed specifically for the custom server called Craftbukkit. Minecraft can only launch its own built-in server, so there's no way (I know of) to have it run Craftbukkit instead when you click "Singleplayer".

However, running craftbukkit locally is totally doable. It won't slow down your machine more than playing singleplayer normally does, because singleplayer runs a hidden server anyway. When you play on a local Craftbukkit server, Minecraft doesn't bother launching its own singleplayer server, so it ends up being the same amount of stuff running on your computer. Of course, you still have to set up the Craftbukkit server and install the Last Airbender plugin properly, but that's doable with some reading and learning. Once you have a multiplayer server running locally, you just use the Multiplayer button, add a server at the localhost address, and have fun.