The best time to get a new bike will vary somewhat due to your region's climate and population density. Bike shops in warmer areas and very large cities are going to sell bikes for sticker price pretty much year round. In regions with a cooler off-season, there will likely be bike shops selling bikes at a discounted price, since they don't move as much stock when riding conditions aren't as nice.
But a pretty universal trend is for bike shops to mark down old model year bikes to help get rid of them and make room for new bikes. New models typically come out between September and November, but some will debut as early as late July, depending on the company.
The best time to look into getting a new bike, then, is usually at the end of the cycling season (mid autumn). You might not want to wait until winter because that's when a lot of shops are looking to keep their stock limited to their best-selling, general-purpose and/or entry-level bikes, since most people don't want to buy anything especially exotic right as snow and ice start becoming a factor (they'd have few opportunities to ride).
If you were to expand your search to used bikes, you would be able to find a whole slew of them in springtime when a lot of people are switching up to new bikes to get ready for a new season.
You may occasionally find two or three model year old bikes sitting in the corners of shops marked down to dealer cost just because it was an odd size or unpopular color, but usually shops aren't going to go super deep on their bike discounts since bike profit margins are typically only between 30% and 45%, and they can't burn up too much of their profits trying to move units.
Your LBS informed you correctly -- Fall is the best time to look for a new bike if you're on the hunt for a new deal and not concerned about the newest and coolest tech.