You can buy cheapo folding bikes. And building a wooden framed bike is likely to cost more given the time and materials, machine time etc needed.I was thinking of folding bike, but these are not cheap, so building a wood frame bike or even a recumbent is a possibility.
Cheapo folding bike Decathlon - £199
https://www.decathlon.co.uk/p/20-in...Vh6ztCh0SQgQvEAQYASABEgJMaPD_BwE&gclsrc=aw.ds