You think she's Filipina and you want to make a good first impression by asking her if she's Filipina in Tagalog. Here's how to do it.
The Tagalog word for 'Filipina' is Pilipina. Filipinos also use the slang Pinay.
Don't assume that every Filipina is fluent in Tagalog. Although Tagalog is the basis of the Filipino national language and is taught in schools, the majority of Filipinos speak another language at home. Your Filipina friend could be Cebuana, meaning she's more comfortable speaking Cebuano and can express herself better in it. She can converse in Tagalog, but don't overlook her pride in her being Cebuana or an Ilocana or a member of any of the many other ethnic groups in the Philippines.