The inland routes we rode didn't have many or deep crossings. Because of our off-road riding skills (read: lack of) we only rode simple tracks. But most inland routes have a lot of crossings.

If they are doable by bike depends on the weather. You have glacier rivers and rain rivers. If it is hot the glacies rivers are difficult and when there is a lot of rain the other ones.

So its best to ask locals, or speak on campsites (hotels are expensive) with fellow travellers with bikes or Jeeps if they used the road you want to ride. We wanted to go Landmanalaugar but a guy with a Jeep told us that if we went there from the south we would have crossings a meter deep so we took a 200km detour and went there up from the north.

On www.road.is you can find the latest road and weather conditions and also if roads are closed because of floodings.

A lot of info about the inland routes you can read in this book. Also how difficult the tracks are.

https://www.islandbuecher.de/shop/ge.../IS3580-detail

Best time to go is from mid-Juli up to the end of August because most roads are open in that period. Before Juli there is still snow in the inlands.

Btw: off road riding besides the tracks is strictly forbiden.