Bike speed is all about power production. Power naturally increases as a passive result of training(especially if you are just beginning), but it can also be developed through more active means. This is the purpose of intervals, higher intensity threshold work, and hill repeats (although these also achieve other physiological benefits).
P = F(v)….power equals force times velocity. The force is the amount of force you exert on the pedals and velocity represents how fast you can turn the pedals over. You can generate more power by increasing either of these. If you are in a gear and spinning at 89 rpms and you increase your rpms to 95 while in the same gear, then this will result in more power and a faster bike speed. The cost to you is a higher heart rate, especially if your neuromuscular patterns have not been conditioned to turn the pedals at this rate(independent of a significant load). Training the neuromuscular firing patterns should be a part of your training.
Of course, training for cadence without addressing power would only have a small impact on your overall speed. You have to address power as well. Completing your intervals, hill repeats and big gear work will help your power. Combining more power with even a small increase in cadence will result in a faster bike split. Your aerobic base will allow you to comfortably sustain the higher cadence.
Your ability to produce power is cadence specific. For example, I have a hard time generating “x” watts of power at a lower cadence. My optimal power generating cadence is 94 – 100. Each person is different and has natural cadence tendencies, but this is also something that can be trained. I bring this up to remind you that your training cadence should be the same as your racing cadence. Specifically, when you complete your intervals, make sure you are doing these at a cadence that you plan to race at. Anytime you race and spend outside of a cadence that you have not trained at, your run will suffer. Make sure you address a variety of cadences as you ride, especially if you plan on doing a course with rolling hills.