Since we travel faster on any bike compared to on foot, these sentences are wrong. The third and fourth will only make sense when you are only talking about those bikes which help us to travel faster. Even in that case, the 3rd and 4th sentences should be prefixed with "those".
A better way to say this is :
Bikes are useful because they enable us to travel faster than on foot
Bikes are useful because traveling on them is faster than on foot
Traveling on bikes is faster than on foot and as a result, bikes are useful.