I suppose it depends on how much variation you want. But think of this: if you have two ways of playing bar 4, 2 ways of playing bar 8, 2 ways of playing bar 12, and 2 ways of playing bar 16, then you have 16 ways of playing the tune.

You can vary by:
Changing the rhythm
Adding notes in the gaps
Using different notes from those "written".

I guess the technical difficulty of these three methods increases in more or less that order.

The basic rules of harmony for writing 2 part pieces are fairly simple and logical. If nothing comes into your head when you play, then a couple of minutes with a sheet of music paper and a pencil will produce some formulaic variations, and you can use those as a basis for something more natural.

I guess few musicians improvise long passages "on the spot". Much improvisation is things which worked before, repeated more confidently, but semi randomly.