"Is it naturally going to happen as I ride more and more, getting stronger with each ride, and pushing myself a little bit more each time I ride, OR is it something you really have to work at?"
Despite being hairs lighter, Kano, you will have to work at it... and work and work and work... it just depends how much faster you want to be and if you have a "fastness level" at which you will be satisfied.
Initially improvements are quick to arrive, it feels easier, more comfortable, takes less effort to get somewhere more quickly. Once your body has adapted to the new demands, it settles in and if you want to go faster you have to push the level occasionally. I outlined a process for this in my first post (oh, and thank you Jiffer for your kind comment
).
The faster you want to go, the more wind resistence you face, therefore the more power your legs have to output in order to maintain or increase your speed. Think about how much faster you can go with no wind, as opposed to riding into a head wind... if you want to maintain the same speed as on a calm day you need to expend more energy...
Here's my example
I now time-trial on a flat course in good conditions at about 31kph. If I double my power output, I could ride at about 40kph, so to get where the level I want be (time-trialling at about 35kph), I need to increase my power output about 70% to achieve a 4-5kph increase in speed.
Now here's the rub... if I ride at 10kph and double my power output, I can ride at about 27-8kph... and increase of 17 kph!!!
On a hill its a matter of doing repetitions... start with two, then three, then five... and remember that each kilogram you lose off you ar your bike will make you 3 seconds faster on a 1km moderate climb
Hope that makes sense...
And to answer your question just one more time... Yes, sorry, but there is no way around it...