Aberrant usage of the adjective "incredulous" [closed]

Both instances are OK grammatically.

In

'You sold the car?' she asked incredulously.

'incredulously' is an adverb, the asking is modified in being unbelievable.

In

'You sold the car?' she asked, incredulous.

'incredulous' is an adjective, modifying the person. She is what is incredulous.

There are in general four positions where an adjective appears in a sentence:

(1) the attributive position: The old car wouldn't start.

(2) the postpositive position (rare): He was driving on the hard shoulder, not the motorway proper.

(3) the predicative position: He was getting old.

(4) in an absolute construction (as here):

'You sold the car?' she asked, incredulous.

Half asleep, he was in danger of falling over the edge.

Cold and wet, we trudged back to the hut.

[note that a single short adjective here wouldn't sound right:

??'You sold the car?' she asked, sad.]

More general absolute clauses are used similarly to add information about the nearest noun phrase:

Her hair flying in the wind, she raced back to the hut.