Bloom is essentially the newbie fairy, learning to use her powers. Bloom also wishes to know exactly what powers she has, what gives her her powers, and where she's from, exactly. While she has nice adoptive parents on Earth, she realizes that she's probably not even from Earth.
Among her clique, Bloom seems to be a natural-born leader, despite being new to the whole "fairy stuff." The other Winx girls look up to her, and see her as their unofficial leader. It is not always for the best, though, as Bloom sometimes makes careless errors that hurt her friends. Bloom also has a tendency to get self-righteous with her friends, which comes off as annoying. And still, she can jump the gun at times, coming to conclusions for no apparent reason.
Still, Bloom tries her best at being a good person, and learning about herself. Her friends probably need to put her in her place occasionally, but overall, Bloom's just trying to be the best she can be.