For one tank it won't hurt.  But don't make a habit out of it. The BMW is
designed for 89 octane, so that's what you should be putting into it.

Shouldn't hurt it but you could run in a few gallons of premium when you
have room in the tank.

Many premium-fuel cars nowadays have knock sensors of one kind or
another that do something to temporarily de-tune the engine (retarding
ignition timing, usually) when knock commences.  I think BMWs have had
this for some years.  Check the owner's manual or look up your make/
model/year (which weren't specified in the original posting) on a
search engine.

Of course, you won't be getting the performance you expect until the
car has the gas it expects, and I wouldn't go in for a smog check
while running the cheaper gas either.  But I doubt you injured the car
at all, especially with just one tankful, unless you've been pulling
heavy trailers uphill or really  putting your foot in the hood
ornament every time the light turns green.  That's what the knock
sensors are for.  BTW, a well-developed spark knock is pretty hard to
ignore, and pretty unmistakably a bad thing that would lead you to lay
off the gas, if you are at all sensitive to what your car is doing.

If knock does commence, putting in a bottle of octane booster and
keeping your acceleration modest (especially on hot days, which
unfortunately some of us don't have much choice about, this time of
year) are good safety measures until you can put in a meaningful
amount of higher-octane gas.  But my bet is that the electronics took
care of it all for you and the symptoms were not noticeable.

Cheers,
--Joe