Road trip to Ladakh sounds amazing , Being a Ladakhi I can give you few insights about it. Road trip to Ladakh can be done via two ways , one from Jammu-kashmir- zojila pass , which is not safe these days with the on going shut down in Kashmir. The other way is via Manali road - Rohtang pass. This would be much more suitable .
Once you reach Ladakh , you will get the biking road details from travel agencies based in Ladakh. safe travels . Happy travelling