Taipei do have a fair amount of good whiskey, e.g. some single malt back from 1967 / Scotch Malt Whiskey Society bottles / Whiskey from independent bottlers. However, most of them that I understands are of single malt / blended whiskey, and mostly from Scotland or Japan.

I didn't really meet bourbons there yet, may be they are available at airport duty free, but surely not a lot. Also kindly remind your mother need to buy it and put it as check-in luggage before heading back to US. Taipei has extreme low tax for Whiskey (they only charge around 100 TWD per liter of distilled liquor) so you don't necessary source it at airport duty free.