The assumption here is that the magnetic field will be strong enough to be affected by steel in the bicycle (frame). Um, think about that for a minute.. People have used compasses in their cars for decades - lots more steel in the chassis than in a bike. The US Army has used compasses with their tanks since the 1910's and did not require the tanker to dismount to do so; tank = big freakin' steel object. You probably DON'T need to actually get off the bicycle to use - at least it in my experience.

Simply riding by a large iron deposit underground can "spin the needle" or at least deflect it from true north. And there are "false norths" in various places in North America as a result of other similar metallic deposits.

So, the reality is - accurate use of a compass while bike touring "depends".