How often do stars pass close (~1ly) to the Sun? Interstellar exchange of massive objects is difficult across several light years. But as the stars orbit the galaxy the distances between them change. I don't find data for neighbor star distances which covers more than a couple of a hundred thousand years. I can imagine that it is difficult to trace their orbits further given todays uncertainties in distance measurements. But I'm interested in a purely statistical/geometrical estimation of how frequent nearby Sun-star passages have been.


How many times has a star come closer than, for example, 1 light year from the Sun since it formed?
How well mixed have the nearest stars become over time? What fraction of them have followed the Sun since formation and made multiple passages?


I suppose that 1 light year's distance is enough to cause disturbances in the Oort cloud and likely exhange comets.
Here is the very study you are looking for by Bailer-Jones (2014).

Using the re-reduction of the Hipparcos astrometry, he has integrated orbits for 50,000 stars to look for objects that might come or might have come close to the Sun.

The K-dwarf Hip 85605 is the winner on that timescale, with a "90% probability of coming between 0.04 and 0.20pc between 240,000 and 470,000 years from now". 

The next best is GL710 a K-dwarf that will come within about 0.1-0.44pc in 1.3 million years.

On a statistical basis, some work has been done by Garcia Sanchez et al. (2001). They estimate, using the Hipparcos data, that encounters within 1pc occur every 2.3 million years. However, the Hipparcos data isn't complete for low-mass, faint objects. Making a correction for this, the authors estimate a $&lt;1pc$ encounter every 100,000 years. The probability for closer approaches scales as the inverse of the square of the separation. i.e. the timescales for approaches closer than 0.1pc is 100 times longer. 

There are plenty of big error bars in all this work - recall that an error of 1km/s in velocity leads to a 1pc error in position after 1 million years. All this should be nailed down really well by Gaia results in the next 2-3 years.