A GPS only gives you a x,y (and maybe z) point. In order to get a direction to compare to North (the definition of a compass) you would need two GPS points. You can either do that by using two points given by a single GPS at different times while you are in motion (giving you a track direction ... something maemo mapper does rather well) or use two or more GPSs with a known relation to you. I don't know of any maemo app that will read two GPSs simultaneously and present the results usefully. I think some survey tools do this and I know that some satellites are using this for rough attitude determination.

A gyroscope will give you your relative orientation. You still need to define a baseline orientation periodically using some external measure. Even the best gyros will drift.

There are electronic compasses that use a magnetic sensor to detect the local geomagnetic field direction rather than the old floating magnetic needle. I don't know of any bluetooth-enabled ones.