As ideas go, this seems quite sensible on the face of it.
Left: Bicycle perambulator: 1926
This looks like a proper engineering job rather than an amateur improvisation. Two tubes run forward from the bicycle end, and hold a swivel that allows the pram to be turned for steering.
There seem to be no brakes on the pram wheels, and one cannot escape the suspicion that this outfit might have been rather short on stopping-power.
This is believed to be Nanny and Child, in Brixton, South London in 1926.
Left: Bicycle perambulator in England: 1926
This was clearly taken on the same photoshoot.
Left: Bicycle perambulator in England: Now
The idea still persists, sort of. This is an Integrated Stroller-Bike. Learn more here.
Seems to me the child would be safer in the original version.