There is a woman in HeartGold who says that if you run through grass you are more likely to "startle" Pokemon as you are making more noise. However, I don't think that running actually increases the number of Pokemon in the grass, nor does it increase the chance that one will appear when you hit each square.
If you are running you are covering squares more quickly, so you should run into a Pokemon sooner. Assuming running speed is twice as fast as walking, it would take about half the time on average to find a Pokemon. (That would also suggest maybe a third or quarter of the time if you are cycling, but in my experience that doesn't seem to be the case.)
