It's called tramlining.  Very common.  The different widths have
less to do with it than the low profile:  /45 front and /40 rear IIRC.
Worn tires cause this effect to be more prominent, as does worn
suspension ball joints and bushings.

FloydR

My wife's 2002 E46 had the problem with its original tires. When I put the
present Avons on, it went away.

This jibes with the experience of all my motorcycle riding friends. Bikes almost
always have different width tires front and rear, and we've all found that  it's
the tread pattern and compound blend which causes the squirm. Some brands and
tire models squirm, and some don't. (We find Dunlops much more likely to squirm
than Metzelers, for instance.) The degree of squirm can be affected by tire
pressures, so you might want to play around a bit.

-- Larry

check for tire wear ... BMWs lose performance before the wear bar indicators
come up I seem to think ... and the car has a way of telling you enough to
ask about it with your mechanic or other people.

think about putting Continentals tires on the buggy ... with the hard road
work you are forced to use ... have your front suspension checked out with
the tires (maybe it is just an air pressure difference but doubt it) for
excessive wear from the hard use.

BMWs are more highway wear, Autobaun actually ... in the USA our roads are
in tuff repair so we have to get BMWs that are tuffer to handled it, tear up
the Jap stuff, or drive Detroit Steel.

sumbuddie wear blind sea

I seriously doubt that a cop would notice the car jumping around as it
follows the ruts in the road. I get that the feeling can be uncomfortable to
you, but on the other hand, you paid extra to have a car that actually feels
the road. You could have bought aa car that feels like a box of pillows
underneath you ...