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Does it bottleneck?

Solution
The i3 4000 series are good because they have hyper threading but in comparison the i3 2000 series are not so good.

GTX 960 will work very well with an i5 3000 series.
Depends if you plan on upgrading your gpu.

The i3 + gtx 970 is better if you don't plan on upgrading the system. The i3 will probably start to bottleneck if you upgrade the gpu.

But the i5 + gtx 960 will allow you to upgrade your gpu in a year or 2 to something much better.
 
It depends entirely on the games you play. an i3 will bottleneck any decent Graphics card if the game is CPU heavy (MMORPGS, and Multiplayer games)
Take my advice and use quadcore+ CPU's if you want to be gaming in the following years