No, You don't have to buy another plugins in order to connect Bamboo with Java or .NET. Please just make sure that you have the right enviroment installed on your system. That means for Java, you will need to have Java JDK installed, for .NET you will need to have the Windows-Tools installed.
Further I would recommend you to work with the Bamboo Remote Agents, because that way your Bamboo server stays clean, while you can use one agent on the Linux server with the JDK for the Java projects and another remote agent on a windows server for the .NET development.
Here you can find more info about that topic:
Please also make sure that you have the MSBuild Plugin installed on your Bamboo version (usually preinstalled on the newer versions).
If you have further questions, just let us know.