Most Helpful Girl
You said she lives in your building, so go to her apartment in person and ask her if she'd like to accompany you to a date. Or, if she just moved, maybe offer to show her around. Speaking personally, I like a guy who's not afraid to speak his mind, but also isn't too blunt. Don't show up and say "I'm attracted to you, let's test the waters" but don't text her either. It should be personal and to-the-point, but not overly enthusiastic (seriously, guys, we know it when you're trying to get something by overly complementing us) or too blunt. Now, if she agrees, great. But if she doesn't, respectfully back off. You can offer to take her around and show her the place, as just friends, but that's about it. If she's not interested, I'm afraid there's nothing you can do2THIS IS NOT RELEVANT ANYMORE
Most Helpful Guy
I think if you have her number, a polite invitation to coffee or something is very acceptable ;)
If she says "no", that's a good time to back off. If she deflects it somehow, you could get away with suggesting another time/activity, or letting her know she can get back to you if she's interested, and then drop it.
Good luck! :)1THIS IS NOT RELEVANT ANYMORE