Yes I went with the BMW, I also went back earlier this year (not with a bike) to watch Eyafjallajökull.
There are a lot of nice areas to drive in Iceland, basically the interior are gravel/pistes. My favorite-area is around Askja, including the road F910 and "old F910". Askja itself is a huge volcano with a hot spring in the bottom. You can climb down and swim, nice! I'll see if I have some pictures somewhere...
Navigation is pretty simple, there are signposts and the maps are good. There is a free GPS-map for Garmin. If you do a search o Olaf's map you might find it, I haven't tried it.
Petrol and food is not to be found everywhere in the interior so it's smart to do some planning. Cold water is easily available, haha!
In May it will be cold and I expect most of the interior to be closed because of snow, ice and maybe lots of water.