I'm thinking of indirectly bribing my son into hanging out with me.
Why do you want to bribe him?
I want to be his friend.
It would be pretty counterintuitive to bribe your child to spend time with you.  You should accept that your role on that relationship is that of a parent not a friend.
I want him to see how smart I am.
Well I'm afraid that paying him to hang out wouldn't really accomplish that.  You should allow him to make his own decisions, but be there to offer guidance whenever he needs it.  He will respect you more as time passes.