lady on wheels
As long as you observe the muslim dress code and/or are unrecognisable as a woman you will almost certainly have no problems. The authorities are tough on their own people, and a little less rigid with travellers so long as you don't set out to "provoke". Cities are obviously more liberal than small towns or rural areas, but even then there can be a crackdown. An EU minister visiting had her chest painted over on press photographs, they are obsessed by skin or hair, but otherwise so friendly.
Riding a bike might offend some male ego's, maybe someone has some experience of this.
Peter, in Oslo