Several guys, including you, have earlier advised to call and see the river. You said it yourself that villain can still bet turn with worse hands and we can improve our hand. By pushing here we would isolate ourselves against better hands only. Did you make some calculations to check that pushing would be better?
Yes, by calling we will leave a insignificant stack behind (20bb), but if villain decides to shove the rest OTR, can we really call if we don't improve? I'm almost 100% sure villain will not risk the rest of his stack with weaker hand than AA.
If we call: we keep villains range wider, we can cut our losses to 80bb.
If we shove: we will risk 100bb, isolate ourselves against a range that we have only 20% equity against. Hands that will fold to shove are probably giving us free showdown if we call so no need to shove as a bluff.