It is a hard choice to carry a guitar or a ukulele. i now have a carbon fiber travel guitar and a carbon fiber ukulele and by all means, especially compared to a wooden instrument they appear indestructible but I still find it hard to believe that repeated vibration on the road, especially if not paved, will not damage the instrument. Alas, I always dream of bringing an instrument with me on a tour - and I NEVER do! :-(
On the other hand it is sometimes difficult to match biking athletes with musically inclined people who like to sing or play. We're out there but there is also a great wall of others who roll eyes when an instrument is procured and who have a talent to immediately start talking when music is played instead of joining in singing, playing etc ... i have many great friends who are like that and You can't blame them. Musical ear eludes some of us.
I do however have a group of friends (unfortunately mostly on another continent) who on trips immediately start participating and then you got a magic happening. Music. People singing and playing and just listening. Sigh. :-)
in the off season I purchased another carrying options for a guitar that I have not tested yet. I plan to test it hopefully this year.