bet on sb/sth的意思是“对某人/某事有信心”，正如我们在中文里常说的“我担保...”。

【例句】
I don't often bet on myself, but I'm trying to think more positively these days.
我通常对自己都不太有信心，不过这些天我都在努力更积极地去思考。

I'm betting on my son to get the job—he's very qualified for the position.
我相信我儿子能得到这份工作。他完全能胜任这一职位。