There was the Welbike (though it was dropped inside a metal canister, not a wooden box).
https://en.wikipedia.org/wiki/Welbike
Some of the links in the Reference Section at the bottom of the page still work.
Others can be found in the internet archives, e.g.:
https://web.archive.org/web/20110930...et/welbike.htm
(The above link has a picture of a bike in a cannister.)
Another bike that was developed (it was to be para-dropped inside a metal frame) was the Royal Enfield WD/RE (The Flying Flea).
It ended up mainly going in by glider, (only a few were every dropped by parachute). It was also carried in landing craft for a beach landings.
https://en.wikipedia.org/wiki/Royal_Enfield_WD/RE