Bay leaf imparts more aroma than flavor. The flavor it adds to a given dish should be subtle. The aroma is mellow, and does a lot to marry more dominant individual flavors.
If you want to get a handle on what it adds try infusing milk with bay and onion the next time you need a bechamel for something. Souffle time? California bay leaf has more flavor than Turkish. Fresher bay leaf has more flavor than old. Fresh bay leaf has so much more flavor than dried, it's almost never used. If you happen to find fresh, figure it at 3 to 4 times as strong as dry. Your experience leads to the inference you may be using older, Turkish leaf which was already old when you bought it. One thinks of European spices as being better than American, but you may want to switch brands and I may want to remember what usually happens when I start thinking.
To make an infused milk, put two Turkish or one California leaf in 20 dl (1 cup) milk, along with 1 small or half a large onion and 6 black peppercorns. Bring to the simmer, turn off the heat, let steep for 20 minutes, then strain. Taste. The taste of bay leaf is what you taste other than onion and pepper.