buckhorn said:
.... How long does it take to develop a sprint?...
Sprinting is as much about technique as it is pure power. Some folks learn real fast and have naturally high NMP others take time to develop. The key thing is to do add some dedicated sprint sessions to your training week, ideally early in the week when you're fresh. Sprint for fixed signposts or other landmarks, not time and if you can sprint against teammates or other riders.
Are short bursts of power for 10- 20s during rides sufficient?
If you really want to develop your sprint then you really should do dedicated sprint workouts with lots of rest between each attempt so that you can give it your best. Some fartlek jumps in a steady longer ride will just teach you to sprint relatively slowly and won't give you the top end speed or technique you need to develop. By all means sprint for city limit signs and the like with friends but start by adding a dedicated sprint workout. Practice small gear sprints for leg speed, big gear for strength and power, lead outs and jumping off a wheel if you can find cooperative partners.
...I have mostly been focusing on climbing hills for training.
Sprinting and climbing are really different beasts with different techniques. I've worked with strong climbers who wanted to sprint like they were climbing a steep grade out of the saddle. That's nothing like sprinting, your body needs to be more compact, tensed, arms flexed and ready to stabilize your upper body but without the rythmic swaying of a climber. You need to coil up and jump like a cat giving it everything right from the start and then spin out your gear to the line. It takes practice but it's pretty fun stuff to work on.
You should also do some work on that one minute power. Realistically most cat 4/5 races come down to a field sprint. You might be a killer climber or have a great jump and VO2 max pace for attacks but the lower cats are amazing at chasing down everything that goes and then sitting up once they reel you in. Bottom line, you'd better have a good sprint but maybe more importantly you need to be able to get yourself up front and into a position from which to launch that sprint. All the sprint in the world won't help if you're twenty riders back and totally boxed in and that happens real fast unless you're willing to get up front and fight to stay there in the closing miles. Picking a good wheel of someone you know will jump is great but in the lower categories it even pays to simply get to the front and stay there at the end. You might get passed by someone sucking your wheel but a top five placing with a clear shot at the line beats a top twenty because you were totally boxed in the closing meters and never got the chance to jump.
Anyway if you're just starting to work on sprints make certain you spend some time working on your tactics for the closing stretch before the sprint winds up. You can do this by leading out teammates during practice while still trying to beat them to the line or doing some VO2max/L6 windups to a sprint during practice but one way or another practice charging the line and then jumping. It's a lot different than the way the pros will do it with an organized team leadout but racing the lower categories is different and almost always comes down to a big disorganized bunch sprint.
Good luck,
Dave