On this page of our guide to BioShock Infinite you will find the second part of a detailed walkthrough of Chapter 38 - Engineering Deck. This particular chapter scene is very short, because it only consists of a meeting with Comstock. You will not duel with him.
The encounter with Comstock may occur after you have broken through the initial enemy groups during your exploration of the Engineering Deck and used one of the sky-lines to reach the upper deck.
Go past the first room found on the top deck and confront Comstock. Once you've dealt with him use the new newly unlocked gate to start moving towards the bridge.