Where did the rumour come from that if you pick a dandelion you'll wet the bed?

They are known in French as pisse-en-lit.

Apparently there are many authorities for what I thought, of which this was one of the first couple I found:

https://www.theguardian.com/notesandqueries/query/0,,-2265,00.html

A yay for the old wives perhaps

Some Irish tinker children that I used to take to school in my taxi-driving days were very amused when I called the yellow flowers dandelions. They called them piss-in-beds. Another slight oddity in their speech was that they would say, 'I done it', 'he done it', but 'her done it'. 'She' was avoided. They didn't want to use a word that's pronounced the same as 'sidhe' - the Irish Gaelic word for the fairy folk.

There are nice pictures of the piss-in-beds at http://www.univers-nature.com/dossiers/pissenlit.html