More than what you are supposed to.

[david11]

And I think it's lovely that we are debating the grammar instead of saying "Cool! Extra money!" and shoving it our pocket and thanking our good fortune. It's nice to see ethics trumping greed.

Oh! Thank you.

I really did it today.

[Winwin2011]

I've learned a lot from the teachers here. However, I'd like to learn some more.

1) Is it natural to say 'The change should be $4, not $5'?
2) Is it natural to say 'You gave me more change for $1 than you were supposed to.
3) How can we make it simple for the difference of "$1'?

Thank you.

[Barb_D]

What's natural will vary from person to person. I would hand the person back one of the dollars and say "You gave me too much" or "You gave me an extra dollar" or maybe "You gave me a dollar too much."

[Raymott]

I've learned a lot from the teachers here. However, I'd like to learn some more.

1) Is it natural to say 'The change should be $4, not $5'? No
2) Is it natural to say 'You gave me more change for $1 than you were supposed to. No
3) How can we make it simple for the difference of "$1'?

Thank you.

Use one of the phrases suggested above, give him back the dollar, and go and sit down.
He's a busy bus-driver. He probably doesn't care.
If he gave you not enough change, it might be more complicated; but remember, he also has a say in how the dialogue goes.