Bus Travel - September

Hi,

My best friend and I are planning a 2-3 week adventure in Iceland this coming September - October

We will have to solely rely on public transport for getting around and so in preparation I am doing research on how we can do this, Iceland seems to have an excellent and extensive bus system however I can't seem to find dates that the service runs on - I read that parts of the roads close down in the winter and some bundle passes I've seen end after the first week of September.

So my question is whether we will have access to the bus service during our stay? And will there be services across the country or just in concentrated areas?

This will be part of our gap year so we are both young and will be working off a serious student budget so tours are most likely out of the price range.

Would you recommend hiring a bike and touring by bike? We'll be hostel-hopping around and spending time in each village/town so we wouldn't be cycling for long.

Thank you!