Three options I can think of -
One - out near where I live surfers carry their boards on their bikes down to the beach by having a side carrier attached to their bike. You will always have to get on adn off from the same side when the unit is attached. But you could easily make one or get one made.
Two - A trombone player friend of mine had a little jig made for the back of her motorcycle that allows the instrument to be strapped to the back. If you have or get a luggage rack for your bike you could from there, here is an example of something someone else did (
http://www.instructables.com/id/Lockable-bicycle-trunk/ )
Three - a dear friend of mine who went to UCLA played woodwinds. She made a backpack type thing that would hold the instruments lower on her back while she rode her motorcycle. I would go to the army surplus store and get back pack parts/shoulder straps. I would get together with someone who sews well, or an engineering type friend and design a basket type thing that will hold the insturments -maybe even have a snap or clasp system to help prevent the insturments from moving. And then carry the instruments backpack style.
<Added>There you go, look below at what Canadian found.
That BAM is the bomb.
