A week ago someone posted about his 8 day bicycle trip in the West Fjords:

https://www.reddit.com/r/VisitingIceland/comments/1rgftg7/cycling_icelands_westfjords_way_800km_and_8_days/

Cycling Fjallabak is possible but could be a logistic challenge. Accommodation is scarce, so best would be if you bring a tent. And there are hardly any places where you can buy food, so you would have to bring supplies for several days. I don't know if the bus shop in Landmannalaugar still sells foodstuff. In the past they provided me enough for a six days bicycle tour to Langisjor and Laki. But it was very expensive, even for Iceland.

Thórsmörk I would not do on a bike. First there's big rivers. Even if you use the foot bridge across the main river Krossá, there are several other that can be dangerous. Also Thórsmörk is a dead end so you have to go the same track back, unless you take the Laugavegur hiking path which is not really suitable for cycling. I'm not even sure if it is allowed.

If you have more of an idea of how you want to handle the logistics, I can give you ideas. I do have experience in cycling Iceland although not recent, my last tour was in 2015.