I suspect that a backpack-style case ought to do the trick, there are some that are hard enough. I've seen people carry double basses like this.
And just saying, in my time in Amsterdam, I was playing in an orchestra. I went to play a concert on foot, and then, when going for a drink afterwards, I travelled in the rack of a celloist friend's bike. He was carrying my trumpet in his back and I, his cello in mine (I do wish I had a photo of it), so one musician and one trombone in one bike shouldn't be that difficult