I'm 17 and recently (about a week ago) bumped into a girl I first met at a party a few months ago where I thought we had a connection, but she was in a relationship at the time so I didn't try anything. Now, however, she is single so this time I got her number and we've had a couple of quite long text conversations (both initiated by me) where she's given reasonably long replies and seemed pretty interested. In getting to know more about her I'm starting to really like her and I'm pretty sure she likes me, based on our texts, which are reasonably flirty, and our first meeting. I'm worried, though, that she's just being nice and I'm unsure when the right time to ask her out is and how I should go about it, especially as she came out of a long term relationship a couple of moths ago.

All you can do is ask her, but how long ago had she gotten out of her relationship. Make sure she's completely over her ex boyfriend before you dive into a relationship. There's no harm in inquiring if she's ready or not but be careful, if you get into a relationship and she still has feelings and has no gotten over her ex properly, you can end up in a relationship going nowhere.

The only way to find out is to ask her, but respect her decision if she is not ready and if she isn't all you can do is wait my friend. Sticking around and not pressuring her will show her you really care and are willing to wait.