First, they are called Mormon missionaries. Second, some of them have cars.
Most ride bikes because 1) they are cheaper than cars (if you don't bring your own transportation, the Church has to provide some for you and bikes are cheaper), 2) it's better for the environment, and 3) it gives you exercise, of which a minimum amount per week is mandated by your "mission president" (the guy who is sort of the leader of the missionaries in your area).
You are correct that it is USUALLY two men that you see out together. But the Church also sends out "sister missionaries" (girls that go out two by two and do the same things the guys do). However, since they are required to wear skirts, they usually get cars instead of bicycles (ever tried to ride a bike in a skirt?). So that's probably why you don't usually see the sister missionaries on bikes.
They go two by two because
1) of Matthew 18:16 ("But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established"),
2) it's more awkward to have 3 missionaries descend upon you than two,
3) it's just easier to assign companions rather than groups,
4) it's more comfortable to be approached by a pair of missionaries than just one (you don't feel as personally vulnerable),
5) it's safer to go by twos than to go alone, and
6) for other reasons I'm probably not thinking of.
Sometimes there will be a group of 3, for example when there is an odd number of missionaries in the area and one missionary is the odd one out, or sometimes for other reasons. But usually they go out in pairs.
P.S. Elderly couples can also serve missions. However, they don't usually do the door-knocking and bike-riding that the young men and women do, because they're simply too fragile. Usually they are the ones who do service projects and help out with the less-physically-demanding work.
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EDIT: No, the women don't always have to wear skirts in the Mormon religion. I'd definitely hate life if that were the case. Women only have to wear skirts when they are serving as missionaries, IF they choose to go on a mission.
