Launch a game and keep up an application that tracks your GPU and CPU utilization. Play the game for a few minutes, then exit and look at what was recorded. Was your CPU over 90% while your GPU was under 85%? Then yes, it's being bottlenecked. Were both over 90%? You're getting the most out of both. Was the CPU under 85% while the GPU was over 90%? Your CPU is actually being bottlenecked by the GPU.
Also note that the FX-6300 only has 3 FPUs and is actually a 3 module, 6 thread part. The extra 3 threads are not "virtual" like with Intel's Hyperthreading, but they are backed by physical ALUs which by themselves are not complete cores.
It could also be a RAM thing, though if you have at least 8GB then it's unlikely. Still worth bringing up CPU-Z and checking to make sure that your RAM is in dual channel mode if you have two modules, and that it's running at the correct speed. There have been times that people post in and have 2x4GB DDR3-1600 but it's in single channel mode and running at DDR3-800. For DDR3-1600, you'd expect CPU-Z to display a clock rate of 800MHz (because DDR is 'double data rate,' the actual clock rate is half the advertised rate; the people who had their modules incorrectly configured at DDR3-800 were showing a clock rate of 400MHz). If you only have 4GB RAM, that could affect things in a similar way.
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