Failing To Yield Charge, Me & A Bicycle

I pulled up to an intersection in which I would have to make a right and merge with traffic already there (morning rush hour) so I had to stop at the stop sign for a while before I could get in. The whole time I'm stealing glances at my side view mirror because there are so many bikes in that area. A spot opens up in front of me and I see a bike coming from about a block away in the bike lane beside me, I knew that if I went I would have enough time to turn and the bike would be no issue. As soon as I do turn, the cop that waits there every morning pulls me over claiming I almost killed the biker and gave me ticket 136(1)(b) but... my issue is that even though I "almost killed" this biker, I knew we weren't really that close to each other, and the bike never stopped at the stop sign! This is my first ticket so I'm kind of crapping my pants but what gives?! I'm fighting it but I'm not sure how to go about it.

Advice would be appreciated.