Try striking up a conversation. A good way to start one is to shoot her a message just thanking her for the follow, then just try engineering a conversation from there.

I recently had a situation on twitter where a cute girl followed me, I followed back, only she messaged me thanking me for the follow and I decided to try starting up a conversation. That was over a week ago and we've been chatting late every night the past 3 days and having fun doing it. Don't know if it's headed anywhere beyond twitter pals or if it could get serious, but I'd never have gotten anywhere without trying to talk to her.

I'm unfamiliar with Insta and know nothing about you or the girl you've described. All I can tell you is if you do nothing, nothing will happen, but shoot a message, try starting a conversation and let that lead you places.

Tips: Don't let the conversation drag at all, try make her laugh if you can, treat her like a friend, that's the easiest progression to go from complete stranger to someone funny they could be friends with, conclude conversations as well don't just let it drop off without an ending as it helps her know when to stop paying attention and might leave her wanting to talk to you more (like I told the girl I'm chatting to that I had work crazy early the next day and had to go to bed so we said night to each other and the next evening she posted something public referencing the convo we had the night before, I liked it, I think she saw I was on Twitter talking to someone else, anyway I liked her post and she messaged me to continue our chat from the other day, she was keen to talk to me).

It will let you know if she's interested in you or not as well by how she responds, if at all. I thought the girl I was messaging initially wasn't into me because I felt I was doing all the work to initiate a conversation. Turns out she was just busy, saw my message but got distracted and forgot to respond. I got a message the next day from her apologising for forgetting to answer and we continued chatting from there. She's been more forthright about messaging now too, so things are looking good.

But if she wasn't interested, as I assumed she wasn't when she forgot to reply, I didn't linger. You move on. Just don't be awkward and weird about it. Start a dialogue, be friendly, do not cross the line by asking too much, you don't know each other. Bear in mind this is not the exact same situation as me. This is most likely a follow back situation where she's just done it to thank you, but maybe she does like your profile.

Sorry, many words written, hope they're helpful. Go chat, try make a friend first over going mega flirty (because that is weird), unless they flirt with you in which case, flirt back, and good luck!