Will a 980 bottleneck a i3 6100?

Solution
I would be looking at Ryzen over any Intel i3/5 right now and even 4C/8T i7s. Yeah it won't bottleneck (unless it is BF1, Watch Dogs 2, Ghost Recon the Wildlands, Rise of the Tomb Raider, GTA V, The Division, The Witcher 3...list goes on so yeah a bit of sarcasm there) but there are much better CPUs for the money that will last a lot longer then a hyper-threaded dual core will in gaming. Not to say you can't game on a dual core but if i was building new PC/CPU platform 4C/8T is the minimum I would aim for ideally 6C/12T. But if budget is to tight I get it but even then you can get a Ryzen R3 with 4C/4T for the price of a dual core Intel CPU.
An i3 6100 can be comfortably paired with a GTX 1060/RX 580. I own an i3 6100 which is paired with a well overclocked GTX 1060, and runs very well. The i3 6100 won't really bottleneck the GTX 980 but in CPU demanding games you will probably want to dial shadows lower, in order to let the processor evenly catch up with the GPU.
 

atomicWAR

Glorious
Ambassador
I would be looking at Ryzen over any Intel i3/5 right now and even 4C/8T i7s. Yeah it won't bottleneck (unless it is BF1, Watch Dogs 2, Ghost Recon the Wildlands, Rise of the Tomb Raider, GTA V, The Division, The Witcher 3...list goes on so yeah a bit of sarcasm there) but there are much better CPUs for the money that will last a lot longer then a hyper-threaded dual core will in gaming. Not to say you can't game on a dual core but if i was building new PC/CPU platform 4C/8T is the minimum I would aim for ideally 6C/12T. But if budget is to tight I get it but even then you can get a Ryzen R3 with 4C/4T for the price of a dual core Intel CPU.
 
Solution
If your going to buy a new budget gaming processor, the G4560 is your best bet. Ryzen 3 is a huge disappointment for gaming and even if Ryzen 5 was in your budget I would suggest going for an I5 7500 for gaming or waiting for 8th gen i5's to be released soon.