I have plenty of bits of paper with notes jotted down .... usually a verse and/or a chorus
Every so often I read through them and (usually) at least one will settle in my mind as a complete song ....... often as something entirely different than what was first intended.

It is better if the whole song comes straight away but even then changes take place ..... fortunately I have very understanding friends at the folk club who let me "try-out" the songs in their various forms.

I find the same process is sometimes required before a tune settles in my head ...... I used to use a tape recorder but then the clips invariably got lost or taped over ......now I use the sound recorder on my PC and keep a file of 60sec sound clips.