Cold is never a problem, if you dress for it. Worse, what you need to keep warm biking in sub freezing temperatures, tend to take up a lot of room. When biking in cold temperatures you end up taking it off and putting it back on depending if you are going uphill or downhill for any long time period. Once committed to such clothing it is easier to store it on the bike then wear it on a bus.
As to wet weather, the gore-tex rain gear keeps most water outside of the gear thus almost never a problem. It is hard for a bike to hydroplane, bikes tires are to narrow. To hydroplane you have to have a tires wider then about three inches. Most bike tires are not that wide, so wet weather, if you dress for it is rarely a problem.
Wind and ice are different stories. Snow is rarely a problem unless it has been packed down into ice. A tailwind is never a problem, it can even get you to where you a biking quicker. Headwinds are another strory, but rarely a problem if less then 10 mph. Above wind speeds of 10 mph you start to run into resistance that will slow most bikers down. Please note l mean constant wind speeds not gusts, gusts are just something you endure till it dies and then you continue on. Winds have to be over 20 mph before winds stop my biking, but then I try to figure out a way to bike where the wind is not blowing that hard. Except in thunderstorms winds tend to stay under 10 mph.
Ice is another problem, ice leads to a loss of traction. The best solution ti ice is studded tires. In winter I use two bikes, one with studded tires and one without. On most days where the snow has been removed I use the bike without studded tires, on days where heavy snows are expected (over six inches) then I switch to the bike with studded tires. Under six inches of snow not worth switching to studded tires, you rarely have ice as the result of such storms along the east coast.
Studded tires do have one huge drawback, you can feel the increase roll resistance di to the studs. That is why I switch between the two bikes (I use to just change tires, but I now have a second bike so I just leave the studded tires on one bike).
As to buses, I find that waiting for one, in bad weather, takes more time then biking. I grew up on the last streetcar line in Pittsburgh and took it to High School, college and beyound, but it came every couple of minutes (it was rare to wait more then two minutes for the streetcar, and if it was packed, wait less then a minute for the next one). You could not fit more people on those streetcars let alone a bike.
I now live in an area where bus service runs once a hour or less. Sorry, it is just faster for me to bike then to wait for the bus. In fact I could bike to my work and back before the first bus had picked up anyone. Thus given the lack of frequency, switching to the bus makes no sense to me. On the old streetcar routes, they now permit bicycles but NOT during rush hour, not enough space for people let alone bicycles. Buses have bike racks and are used, but only on routes where biking is slower the the bus including waiting and loading times.
Sorry, in most cases bus transportation is not that much of an improvement over biking, even in bad weather.
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