Aria is being kind to Annie in her own way.
If Annie just follow her feeling, she will face with a man who like her master, and only meet Annie to know more about Aria, and even may hurt her feeling more and more. To Burboom currently, Annie just a maid of the pretty woman he like. Her pretty face will make him want to play around with her, but marriage to a maid is not his top choice.
But if Annie target Burboom as a wealthy handsome social man, she will weight his value against her own. This will improve Annie confidence, as she is Aria Roscent's maid, if Burboom love her, he will gain Aria support and a beautiful girl's love. If he do not, Annie still the proud close maid of Aria, while he get nothing.
This knowledge will help Annie make better decision, and better tactic. Instead of giving Burboom benefit to lure him, she can show him how Aria is out of his league, while having friendly approach and wait for him to drop his expectation, then show Annie own beauty, Annie position, Annie value as link to Aria's power. That will make Burboom want Annie as his wife.
Of course, this kind of help only work with Annie anyway. She has a similar view of value as Aria.