Well, I was an active JW, and then converted to Mormonism. As a JW I was quite used to knocking on doors in field service. So when I became Mormon, I also did local missionary work, including knocking on doors with young full-time Mormon missionaries. Typically, the one I worked with were from Utah. They all wore white shirts and ties, but also full suits. They were always clean-cut and friendly. I never used to see them with shirts and ties only, but now it seems to be all that I see. I suppose the climate has a lot to do with it, because if it's in a colder area, I'm pretty sure they would be wearing full suits, as well as coats.
I went door-to-door with the Mormon missionaries in a small town (3,000), as well as a medium (20,000+) and large city (600,000+). In the small town the Missionaries had no car, and no bicycle. They walked everywhere. If they worked in the countryside, they would do so with others who had cars. In the medium sized city they still walked a lot, but also had bicycles. They often accompanied others like myself who did have a car. One way or the other, they got the job done. For the big city, it was not unusual to have a car available, but there were also a lot of buses utilized. Again, they would work with others who did have cars.
As I recall, nobody made a big deal about this.They had a lot more on their minds than issues of transportation. Constant prayer meetings and church meetings, studying the Book of Mormon, learning their presentations, following up leads and conducting the missionary discussions with householders, being accountable to their Mission President and Church Leaders, writing letters back home, and on and on and on. During this two year period they also spend a lot of time focusing on fasting and prayer, trying to develop a closer relationship with God. This is not a game of pretence for them, and you have to try fasting and prayer for an extended period of time to find out just how challenging that can be. That would weed out the pretenders pretty quickly.
Each missionary basically does their own financing of the two year mission. Or I should say that in most instances it is the parents who must do the financing. Now, if the parents cannot afford these costs every month, then the Ward where they reside kicks in and finances this missionary either in whole or in part (if the parents have some money, but not enough).
Nowadays, it has become a very expensive proposition to own (or rent) and operate a vehicle. I can understand why bicycles would make sense, moreso now than in previous years. Also, have you noticed in large urban centres how couriers prefer bicycles to cars. They can run around block after block, weaving in and out of traffic. Cars get stuck in traffic, gridlocked, parking is impossible and expensive. It is so much easier and practical with a bicycle.
Now, of course, I no longer believe in Mormonism, and left back in the 1980's. You may question the motives of the Mormon missionaries, but I just don't think the matter of riding around on bicycles is in any way done for appearances sake, creating the impression of self-sacrifice and all that. It's more about practicality and economic reality. It's probably because you see them everywhere all the time, looking just the same as every other one; just that you pause and wonder their motive(s). But really, this is just a kind of stereotyping, IMO.
It's just not a big deal, particularly for them.
Rod P.