...will fit on my 2001 528i bmw? Which size tires will be best to wrap those 20x9.5 rims without rubbing or constrict turning.

Yes.. assuming your BMW is a 2001 525i you can put 20x9.5 wheels on it. Incidentally, they did not make a 528 in 2001, it was the 525 then, but yours may be a different model year 528. Either way, the recomended tire size is 245/35 R20.

Go to www.tirerack.com and pick your wheels and/or tires. The BBS CK is an example of a 20x9.5 that will work.