Last time I made ginger ale, I was brewing professionally. But my method will work just the same in homebrew.
I brewed a batch of Special Bitter. Nothing over the top, just Pale and 55L Crystal malt to 1.044, Challenger to 35 IBU, finished with Goldings. Racked 5 gallons into a corny keg for use on the pub's handpump. Tossed in about 4 oz of ginger in a cheesecloth bag. Let it steep for two weeks, then started serving.
People raved about it. Kicked the 'cask' in about three hours.
So, my advice is to 'dry-hop' in the secondary if bottling; add it to the keg if kegging. The character will change over time.