I agree with what most have said here. I began ridding (again) last July. With saddle time naturally comes speed but the other side benefits of saddle time comes, for a lot of us, weight loss which perpetuates more speed. Like the dog chasing it's tail.

I've gone from a mostly 12-13 mph average last year to more 15-17 averages just by looking at my spreadsheet. A 15 mile ride last November was ~15 mph. March of this year that same ride will be ~17 and a cadence of ~90 according to the Polar HRM/cadence deal.

Look for climbs, sprint to the next mailbox, do individual time trials trying to beat your personal best, spin to get your cadence up, look for a group to ride with that's faster than you (my quest now).
All of these, in my opinion, will get you faster. I want to be the (old) guy that shows up for a 50 mile group ride on my 34 lb mountain bike and have a 16 mph average.

Then there's that going back and getting better genetics... I'd like to get on that bus trip.