No one who has answered so far has given the obvious explanation that in this context "being bent over" is describing bending forward at the neck to stare at his phone. Saying that he spends too much time in this posture is in indirect way of pointing out that he's addicted to using his phone.

Bent is sometimes used to describe a state of anger or intoxication. in your example the right way of using the Grammar would be "bending over his phone" although that is not the most common thing to say in vocabulary. some times getting bent is used in sports, for example, you can say this player got bent by that player.(we say that a lot in Football) It is sometimes used as describing motivation: "she was bent on getting married"

You can remove "being" from this sentence. "He spends too much time bent over his phone."

It doesn't really make sense, to be bent over means your in a position, as if you were stretching or trying to pick up something from the ground. So it's something you do just for a little while, you don't stay that way for long. So it really doesn't make sense to link that with the phone. Can you explain what you were trying to say?