"Bal tashchis" is a prohibition on destroying something for which there is potential use. Destroying something that has no use is not in violation of that prohibition. Because there is no use for separated chala (because, as you note, there's no one around these days who can eat it), one may destroy it. Moreover, one can separate the chala even though it will wind up destroyed, because fulfillment of a mitzva is a valid reason for destroying something: it does not violate "bal tashchis".
Source: This is common knowledge of the prohibition of "bal tashchis". One example source is the Chinuch (529), who writes (in my own loose translation) "...but certainly it's permissible to cut them [=fruit trees] if he finds a purpose in doing so... and any non-fruit tree, [the rabbis] said, one may cut even if he doesn't need it...". As an example of the permissibility of destroying something for a purpose, Mishna B'rura 560:9 writes that it's permissible to break a cup at a wedding "since they do so as a hint to a lesson, so people place it in their hearts".