And then, can I say, "I'm happy helping you." instead of "I'm happy to be helping you."? If this isn't idiomatic one to your ear, what is the difference?
Both are correct. Grammatically, in:
- I'm happy helping you.
"helping you" is an adverbial that indicates the time or manner in which "I" feels happiness. Notice you can place it in front position:
- Helping you, I'm happy.
- I'm happy to be helping you.
"to be helping you" complementizes "happy" and seems to me to express the reason for "I"'s happiness.