This road descends 440 m over 12.8 km. Downhill it's absolutely an option. And in this particular case I don't see OK alternatives for road bikers from the map. Maybe via B500 (also a Bundesstrasse) K4907 and L128, but it's a 8 km + 150 m climb detour.
Uphill I see how it's probably not fun and one should rather take some light gravel even on a road bike.
 Also I'm reasonably sure it's obectively less unsafe to be cyclist on a 2-lanes-per-direction road then a 1-lane-per-direction road  when both are busy with cars.