transporting unicycles

In Canberra when I used to play unihocky on Sunday afternoons, I was one
of many players who biked to the game. A few options were favoured. One
involved strapping the stick to the top bar of the bike and strapping the
unicycle to your backpack. I also became quite proficient at simply
cycling with my 24" wheel hanging off one handlebar. I normally carried
the seat in my backpack to avoid it dragging along the ground. One guy
even used to just balance the uni on his back and cycle a few kilometres
to the game.