The new dress becomes you.
would be better than either of the sentences you mention.
The Google Ngram Viewer has some results for "dress becomes you", and none for either "dress is becoming with you" or "dress is becoming to you".
This question relates to an idiomatic, somewhat rare use of the word "become". While this verb normally is dynamic and means that the subject is in the process of turning into something else, or gaining some attribute, it can also be used as a stative verb with the meaning that the subject makes something else look good.
When the verb "become" is used this way, it takes a direct object with no preposition. Here are the two examples from the Oxford Dictionaries entry:
‘the dress becomes her’
‘In her monastic habit she looked coarse and overblown: the severe lines and sober tints of the dress did not become her.’
As you can see, since this sense of "become" has a stative meaning, the idiom is to use the non-progressive form. We don't use the progressive in this construction (with a subject, a form of "become", and a direct object):
- *the dress is becoming her (incorrect)
- *the severe lines and sober tints of the dress were not becoming her. (incorrect)
"Becoming" as an adjective can be followed by "on..."
Even though the progressive aspect is not used for this sense of "become", it is idiomatic to use the word "becoming" without an object as an adjective.
I was about to write "I don't think 'becoming on you'
is used with the verb 'is' ", but as Chaim points out in a comment there are actually many examples of this.
So it seems
The new dress is becoming on you.
would also work. However, I still don't like the sound of this as much as my initial suggestion of "That new dress becomes you."