I've 56 and been riding for a year now. Roughly 4k miles. 500-600 miles a month when it's warm. My overall average speed is right at 15mph in the moderate hills of middle Tennessee.
A month and a half ago, I bought a drop bar bike thinking it would increase my speed. Well, it doesn't

I may be 1/4 mph faster on the same 1 or 2 hour loop as I am on my hybrid. So much for that idea!
So, I'm wondering, does increasing your speed come with time or do you have to work at it, working out and such, to get up into the 18 or 19 mph average range? I know guys my age that have been cycling a long time that do it all the time. Since I'm starting late I don't know if it just comes with time or requires work. I'm not much of a worker. Ha!
If I did want to work at it, what kind of training should I be looking at? I'm in a lot better shape than before I started riding and lost 10% of my weight, currently 200 pounds, but the speed just isn't coming. It's not
that big of a deal as I ride mostly for fitness and enjoyment, but one of my goals is a century, so a faster speed would help in that regard. I've done a couple of metrics now, but thinking about doing half again that much just isn't happening right now