Admitted to going 80 in a 55 out of panic during the stop. cop got me at 82 on radar

In Suffolk county, New York. Got caught going 82 in a 55 on sunrise highway. Cop gave me a ticket, he asked me how fast I was going and I panicked and told him 80. I know this was the stupidest thing for me to do, I had good experiences with cops letting me go before, so I just was honest but I (deservedly) got a ticket this time. I know NY, specifically Long Island is very lenient on moving violations and will almost always plea down especially as a first timer, but if I’m pleading not guilty, and I more or less admitted it at the traffic stop, what do I do when it gets to trial, and at what point am I offered a plea bargain?