Hola, Susana. First, understand that I am retired and live in Isla de San Andres; however, I visit Bogota whenever I can, and I am just ending a 6-week stay here. I am considering moving here - at least part-time - and have been exploring. I have sort of attached myself to Av Carrera 7, and areas convenient to it, North and South.
I absolutely love Chapinero, both Alto and "normal" or "principal," more occidente; Teusaquillo, of course La Candelaria; for the latter, there are still reasons to be vigilant at night; the area has been greatly rehabilitated but there is still some street crime for the unprepared. I have family and friends that are living in Centro, so even there, safety has improved greatly, but as a young woman, no matter where you live, you will have to become very "street-wise" to feel comfortable and safe as you learn this great city.
Further north, Chico and Santa Barbara are very nice and you can find affordable housing if you look closely. Then, a little further north and west - nearer the Autopista Norte, are other more affordable areas...Santa Barbara extends in that direction, and there is Palomino and Alhambra.
I have stayed in these areas because they are closer and more convenient to the apartment of my suegra in the beautiful barrio of Rosales, where I am based when I visit Bogota. Bus and taxi service is very convenient on La Septima, and there are many centros commerciales in the area: Andino, Atlantis, Avenida Chile, etc., plus Carrulla's, Exito's, and many tiendas and almacenes.
One quick source for your research is on Facebook, a page called "Bogota Short Term Rentals." There are many apartments for rent there, although based on the posts from readers, there seems to be a lot of interest. Maybe other readers here will provide other sites for you to search. It seems there are many options for sharing apartments; I'm sure that you can find something suitable, but you just have to find the right person or small group to suit you. Due to the size of Bogota and safety concerns that go along with living in any large city, it might be good for your to live with, and learn from, other folks, especially women...I love Bogota; during my first visits, I didn't like the congestion, the traffic, the rain...but I have come to love this city. You become accustomed to the changing weather, the traffic, even los trancones...they become part of life here. Bogota has many opportunities for enjoyment: Bars, restaurants, museums, music, and is very convenient to paseando en la savana for day-trips or weekends.
Good luck with your search, and the new life you are creating for your self.
Wally