Bus bike rack too short, how to strap in a bike quickly?

Couldn't believe it. Those great agency folks obviously didn't test the
bike racks for our local buses before signing the contract. Long story
short my 29er bike didn't fit in and neither did my friend's. Luckily
the driver was patient and helpful. We had to load the bikes reversed so
the hook goes over the rear wheel. Not easy because of my panniers but
worked, somehow. The front wheels now rode up on the other side of the
rack slot. We both had bungee cords with which we strapped them down as
hard as we could. Oh, and the slot width barely fit my 2.25" wide MTB
tires barely squeezed in and I had to push down hard. The rack looks
like this:

https://ixquick-proxy.com/do/spg/sho...8df2678ec2064b

When we arrived another rider put his 26" MTB on there on even that
barely fit in (rear wheel rode up half an inch).

Does anyone know a better "strap down" method that is faster than
wrapping a bungee around rim and rack numerous times?

--
Regards, Joerg

http://www.analogconsultants.com/