>>Try and become friends with her
Are you fucking insane!?
OP, you already made a misstep by getting her screen name and not her phone number. Get that as soon as possible and ask her out on a date in one week. During that seven day waiting period, keep your contact with her to a minimum. Go somewhere neutral and public, like a mall.
NOW you can talk with her about anime all you want but don't forget to ask her about other important things, like what else she likes to do. DO treat it like a date, DO NOT act like two friends chumming around the mall.
Update us from there