I have a mountain bike, and I wonder if I can develop my abs if I take my bike to work everyday.
Cycling up hill will do this. Although it's not too intense a work out. Ride standing up and you'll use the required muscle group for balance (as a person standing is harder to balance than one sitting, and thus uses more muscles). Since you're sitting symmetrically this will also give you an 'even' work out.
So just modify your route to take in a couple of small hills. Fartlek is best (basically - alternating intensity during exercise to stress your body), so flat then hill then flat then hill.
As others have pointed out cycling is an inefficient way to exercise the muscles in your core. Cycling will utilize those muscles and your cycling performance will likely benefit from strengthening them - but cycling specifically won't really build strength in those muscles, you have to work them off the bike.
This article from Bicycling covers the topic pretty nicely and has links to some great core workouts for cyclists. Personally, I've used the exercises described on here and they're pretty good.
You could always opt for a rowing bike. That would probably work your abs more than a regular bike.
What most people mean by developing their abs is that they want their abdominal muscles to show through their skin, commonly referred to as a six pack.
While you probably wont engage your abdominals in cycling very much, cycling as an endurance activity will increase your caloric needs and make it easier for you to reduce the amount of body fat covering your abs. The common misconception that you will lose fat in the trained area is a myth. Of course you still need at least some abdominal muscle mass for it to show, but losing the fat that covers them is harder than training the core. And while I think that cycling is a good idea to get rid of some fat, a healthy diet can have an even bigger effect on your overall body fat percentage.
Adding to that there is a debate in the fitness community if specific training (aka isolation exercises) for the abs - such as crunches - is a good idea at all. The current trend prefers exercises that engage the whole core, reducing the negative effects of muscle imbalances.
For example: My main exercise for the abdominal area currently are chin-ups and pull-ups. While the movement doesn't seems to have a lot of core-engagement in the first place, I am not the only one who is convinced that they are a good core exercise. On T-Nation is an article comparing different ab exercises, chin-ups were one of the top exercises.
Probably the most shocking result of this entire experiment was the level of rectus abdominis activity elicited by a bodyweight chin-up! It beat out any other abdominal exercise, weighted exercises and all, in mean and peak rectus abdominis activity.
[…] If you're aiming to get a great core workout via chin ups, I recommend performing slow, controlled repetitions while focusing on keeping the hips and spine perfectly neutral throughout the set.
I would suggest a two fold approach! Firstly ride your bike in a fat burning zone. Your going to need to have a relatively low body fat percentage if you want to have decent muscle definition. So I'd take the long route into work!
The second phase is once you arrive at work jump off your bike and do some sit-ups, once your strong enough you could use your bike as additional weight whilst performing some crunches.. Alternatively a structured weight routine in the gym would work.
Your not going develop a killer six pack by just riding a bike though I'm afraid!