If Dick has an Aunt, why does he live with Bruce Wayne?

It probably helps to know the "history" from the comics. Dick Grayson had been Bruce Wayne's ward since 1940, but Aunt Harriet was only introduced/created in 1964. And the circumstances of THAT were, she came to live at Wayne Manor to help with the house after the DEATH of Alfred. It was shortly after that that the TV producers formulated the series, and they decided they wanted both characters, and soon after, Alfred was bizarrely revived in the comics to conform to the TV continuity.

I'm sure that a wealthy man like Bruce Wayne was simply trying to help Dick Grayson's elderly aunt and make sure that she was being provided for too.

It was because of the perceived homophobia of the 50's and 60's that they included Aunt Harriet.

I thought Harriet was Bruce's aunt

hmmm  Always thought she's Bruce's Aunt also - and Dick's by extension - but you do have to figure in another factor into the equation.

And that would have to be that the poor lady has failed so miserably with Larry Mondello - that she finally gets to redeem herself by rearing Dick Grayson into a hot and really obedient Crimefighter.

How many times to you hear her saying, "Now, Larry Mondello, you just wait until your father comes home?"

But do you ever even once hear her have to say, "Now, Dick Grayson, you just wait until Bruce gets home." - Zilch.

Okay, so maybe Bruce and Dick enter and exit together most of the time anyway - but big time trouble follows Dick and Bruce around whereas Larry Mondello gets into his own trouble pretty fast all right.

Therefore Madge finally gets her chance to raise a kid right even if Alfred and Bruce have to do that for her, right?

 Mellow Salutations!

I think Bruce let her move in because she was Dick's aunt and since both had lost their parents at a young age it would give Dick a family connection. Off the subject I remember in Batman 89 when Vicki asked Bruce about his family he replied that Alfred was "his family".

Because Wayne Manor was too big for Bruce to live by himself in

The character was included to answer the question:

"When do Bruce and Dick have time to cook, wash dishes, do their laundry, vacuum the house, clean the bathrooms? etc."