When I was a kid, I thought the bridge was at the bottom of the saucer. I have no recollection for my reasoning, maybe because it was closer to the phaser banks?
I had something similar. I first became a Trekkie at age nine when my dad took me to see TSFS in the theatre when it first came out. It was over the next year or so that my dad would videotape TOS reruns on VHS, and that's how I finally built up my TV collection while I was waiting for the next movie to come out.
My only other exposure to Trek at the time was the Pocket Books novel series -- when the story had the characters going to the Bridge, I initially thought it was an actual, literal bridge like you see over a river.