Hi Niklas, In general, I would recommend starting in the south because the prevailing winds are from the south, so heading North will give you more tailwind.
However, you should always check the weather forecast (www.yr.no/en). Where is the driest and warmest? Right now, the North is experiencing high pressure. Bodø is nice and warm for the next 7 days. And as you write, when you start heading south, you will be riding, in theory, to a warmer climate as Autumn hits.

But how do you get to Bodø from Bergen? The only way is to take the boat, which will take a few days (or fly).

Note, you can easily reverse the routes with a few clicks. More info on the routes here: http://www.youtube.com/watch?v=hk3LkZ1SArU&feature=youtu.be