New Jersey.

I am planning on putting up a fence approx 2ft inside my property line. The current property line runs down my neighbours driveway 1ft away from my property.

Am I at risk of giving up the land due to adverse possesion, the land is covered by 6ft high bushes that I maintain, but the fence will be inside these?.

Would putting a gate giving access to the Neighbours driveway and my 1ft strip of land make a difference?

Why would you put a fence inside bushes that are on the proeprty line? Aren't the bushes the boundary? It is up to you what you do, but you may want to consider removing the bushes, then putting up the fence. You may want to ask the neighbor to buy the 1 ft of land they own, or just give it to them. Consult a local attorney but I think some common sense may be in order too.