Permissions are done at a project level, not issue type.
You can do it with a bit of code, although it is quite blunt. If you set up an "issue type security scheme", you can use post-functions to set a security level differently according to whether it's a bug or support request (either by writing code that checks the issue type, or by having two separate workflows with different functions). You could also do this with a listener, although they're a bit harder to code and slightly risky on service desk as they may not set the level fast enough.
As I say though, this is blunt. A security level can only control issue visibility, you don't get individual permissions like edit, transition, close etc.
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