Update:
I took it to the dealer. His Fault Code reader said the transmission shifter selecter switch (on the side of the transmission) was suspect, as was the wiring harness. Mike Miller at BMW CCA sent me some info on a recall of that switch, which described that in a failure, the transmission could shift down, but not up. So I bought a new switch from the dealer, put it in, and fixed the problem! HAPPY!
Bruce in FL