Junebug: I'm always afraid if I take a fall on the bike, that Yoda will suffer a worse fall.
Perhaps there's some way to strap them in? Such as a something tied to their harnesses?
That said, we have put him in a little basket and he generally stays (when Yoda is high up off the ground, he'll generally stay put). The basket is pretty high, perhaps a foot? And he was only ridden around for a little bit in our driveway or his grandparent's property with grass everywhere. He likes the wind in his hair, that's for sure!