How did an evening at the ball offer Mme. Loosely a chance to present herself in a new guise?

Guy de Maupassant establishes some critical details for his leading characters in his first few paragraphs. Mathilde is described as a young woman of humble means who is frustrated and ashamed of her social status. She is deeply concerned with appearances, and is tormented by the fact that she is unable to live in the kind of wealth and splendor enjoyed by the highest classes. That is what she aspires towards, and yet it is clear that the reality of her life does not match her ideal of what she wants it to be.
Then we come to the subject of the party, and it's important to note her initial reaction, because here that obsession on appearances and impressions is expressed strongly. She actually rebels against going at first, and needs to get a new dress, and after her husband gives her the money to buy one, she then needs jewellery too. Here we see her focus on those appearances, combined with her anger and shame about her own humility. She cannot go to the party unless she can do so while creating the impression of being a member of the elite.
And that's the guise your question asks for. When Mathilde goes to the party, she takes on the trappings of wealth and status for herself, but in this, she's actually taking on a lot more than a simple guise. You're seeing here her deepest aspirations: everything she wants to be but isn't. The party gives her the opportunity to live out that dream.