First of all a "bottleneck" means a component that is slowing things down.
If we translate to mean:
"are there games for which my GTX960 can't output 1080p, on max settings, at 60FPS" then the answer is... YES. So, NO, your monitor is not a "bottleneck" in this sense.
Even if you had a top-end CPU there are plenty of games that your computer can't run at 60FPS, 1080p on max settings.
If you had an older game and a 144Hz monitor then you could output 144FPS so sure in that sense, for that game, your current monitor is a bottleneck to what displayable FPS you might get.
Make sense?
In the future you might want to consider a GSYNC monitor when prices drop.