Time yourself exactly as you pass various waypoints. See where you're losing time. Obeying traffic laws will certainly cause a terrible loss of time.

Just becoming aware of the slow parts might be sufficient.

If you're not fitting the bike, or are carrying lots of stuff, or dressed in a slightly less efficient manner then your speed will drop. I'm much much slower on my commuting bike:

More weight
Less lively geometry
More upright position
No clipless pedals
Wider tires
More air resistance

Just makes the whole experience that much less quick. I probably average 12 mph on my commuter vs. 18 mph on my real bike.