Bounce in this context is very colloquial, so the way it's phrased is not 'normal' English. But there are similar phrases which have the same format and similar meaning in English, such as 'Their Dad ran out on them.' (Their Dad left/abandoned them), 'I skipped town on them.' (I left the town they were in), 'My Mum snuck out on us to go to a party!' (My Mum left without telling us to go to a Party) The implication here is that the person leaving has made a choice, but the people he/she has left are passive, because they are being left behind.
If I had to guess at exactly why ON is used in these phrases, I'd say it's because when something is Over/On/Above etc. something that usually implies height, or superiority, so by doing certain things ON someone, rather than TO/AT someone it makes the subject of the sentence seem more powerful than the objects, rather than equal.