The idea of this route is to make it to Birkkarspitze on one day, using only the German trains and a not-state-of-the-art bike. Thus it is a bit longer than going through Karwendelhaus but the bike part is (I assume) much less tiresome.

The route goes like this:

* [bike] Mittenwald to Kastenalm - 21 km, 300 hm 

* [hike] Kastenalm to Birkkarspitze - 3 km, 1500 hm

* [bike & hike] Birkkarspitze via Kastenalm (hike down) and then back to Mittenwald on the bike

Description

Start in Mittenwald to Scharntz is on the Isarradweg, which is quite nice and relaxed and offers no challenges. Still, it is not asphalt and a bike with wider and more stable tires would be better. In Scharnitz we find to way in direction of Isarquelle/ursprung - it's where the river starts and there is information and shields about it. The way itself is rather popular in summer, wide, very mellow going up but especially here mountain bike tires are reccommended (according to my memory of the way).

From the Isarursprung on we leave the bikes and start the hiking part of the tour which is more demanding: 1500 hm on 3 km suggest a rather steep way up :) I ahve not done this part myself, according to an online description it is well marked way through the Birkkar till the Biwak-box. After that it becomes a way secured with steel rope for around 100 hm till the peak. From Birkkarspitze there should be a wonderful view of the Karwendel. 

Descent is on the same way, collecting the bikes after we are done with the steep part and cycling back to Mittenwald. 

Time estimation: realistic is ca. 5-6 hours for the hiking part and 2-2,5 hours for the biking, so in total a minumum of 7 hours in movement, I would rather plan the day with 8-9 hours.